Init

.idea/.gitignore

@@ -0,0 +1,8 @@
+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

EuclideaGame.py

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+import pandas as pd
+import datasets
+from datasets import GeneratorBasedBuilder
+
+
+class EuclideaGame(GeneratorBasedBuilder):
+    def __init__(self, levels=None, **kwargs):
+        super().__init__(**kwargs)
+        self.levels = levels
+
+    def _info(self):
+        return datasets.DatasetInfo(
+            description="This dataset is a collection of the Euclidea "
+                        "geometry game levels, alongside their provided solutions.",
+            features=datasets.Features({
+                "level_id": datasets.Value("string"),
+                "question": datasets.Value("string"),
+                "solution_nl": datasets.Value("string"),
+                "solution_tool": datasets.Value("string"),
+                "solution_symbol": datasets.Value("string"),
+                "initial_symbol": datasets.Value("string"),
+                "pack": datasets.ClassLabel(
+                    names=["Alpha", "Beta", "Gamma", "Delta", "Epsilon", "Zeta", "Eta", "Theta", "Iota", "Kappa",
+                           "Lambda"])
+            }),
+        )
+
+    def _split_generators(self, dl_manager):
+        """Point to local file path within the repository."""
+        return [
+            datasets.SplitGenerator(
+                name=datasets.Split.TRAIN,
+                gen_kwargs={"filepath": "data/EuclideaGame.csv", "levels": self.levels}
+            )
+        ]
+
+    def _generate_examples(self, filepath, levels=None):
+        data = pd.read_csv(filepath)
+        if levels:
+            data = data[data['level'].isin(levels)]
+        for idx, row in data.iterrows():
+            yield idx, {
+                'question': row['question'],
+                'solution_nl': row['solution_nl'],
+                'solution_tool': row['solution_tool'],
+                'solution_symbol': row['solution_symbol'],
+                'initial_symbol': row['initial_symbol']
+            }

data/EuclideaGame.csv

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+pack,level_id,question,solution_nl,solution_tool,solution_symbol,initial_symbol
+Alpha,https://euclidea.fandom.com/wiki/Equilateral_Triangle,"Description: Construct an equilateral triangle with the given side. The construction must be exact. Guessing even very close points does not count as a solution.Let A and B be the two end points of the given segment.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center A and radius AB
+<Circle Tool>Construct a circle with center B and radius AB, intersecting circle A at points C and D
+<Line Tool>Construct line AC
+<Line Tool>Construct line BC","['Circle Tool', 'Circle Tool', 'Line Tool', 'Line Tool']","[['A', 'B'], ['AB'], ['C', 'D'], ['AC'], ['BC']]","['A', 'B']"
+Alpha,https://euclidea.fandom.com/wiki/Angle_of_60%C2%B0,"Description: Construct an angle of 60° with the given side.Let A be the initial point of the given ray.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center A and an arbitrary radius, intersecting the ray at point B.
+<Circle Tool>Construct a circle with center B and radius AB, intersecting circle A at points C and D.
+<Line Tool>Construct line AC.","['Circle Tool', 'Circle Tool', 'Line Tool']","[['A'], ['B'], ['C', 'AB', 'D'], ['AC']]",['A']
+Alpha,https://euclidea.fandom.com/wiki/Perpendicular_Bisector,"Description: Construct the perpendicular bisector of the segment.Given the segment AB.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center A and radius AB.
+<Circle Tool>Construct a circle with center B and radius AB, intersecting circle A at C and D.
+<Line Tool>Construct line CD.","['Circle Tool', 'Circle Tool', 'Line Tool']","[['AB'], ['A'], ['C', 'B', 'D'], ['CD']]",['AB']
+Alpha,https://euclidea.fandom.com/wiki/Midpoint,"Description: Construct the midpoint of the segment defined by two points.Let A and B be the two points.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB.
+<Perpendicular Bisector Tool>Construct the perpendicular bisector of AB, intersecting AB at point C.","['Line Tool', 'Perpendicular Bisector Tool']","[['A', 'B'], ['AB'], ['C']]","['A', 'B']"
+Alpha,https://euclidea.fandom.com/wiki/Circle_in_Square,"Description: Inscribe a circle in the square.Given the square ABCD.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC.
+<Perpendicular Bisector Tool>Construct the perpendicular bisector of AB, intersecting AB at point E and AC at point F.
+<Circle Tool>Construct a circle with center E and radius EF.","['Line Tool', 'Perpendicular Bisector Tool', 'Circle Tool']","[['ABCD'], ['AC'], ['F', 'AB', 'E'], ['EF']]",['ABCD']
+Alpha,https://euclidea.fandom.com/wiki/Rhombus_in_Rectangle,"Description: Inscribe a rhombus in the rectangle so that they share a diagonal.Given the rectangle ABCD with AB>AD.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Bisector Tool>Construct the perpendicular bisector of AC, intersecting AB at point E and CD at point F.
+<Line Tool>Construct line AF.
+<Line Tool>Construct line CE.","['Perpendicular Bisector Tool', 'Line Tool', 'Line Tool']","[['ABCD', 'AB', 'AD'], ['F', 'E', 'AC', 'CD'], ['AF'], ['CE']]","['ABCD', 'AB', 'AD']"
+Alpha,https://euclidea.fandom.com/wiki/Circle_Center,"Description: Construct the center of the circle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the perpendicular bisector P1 of two arbitrary points on the circle.
+<Circle Tool>Construct the perpendicular bisector of two other arbitrary points on the circle, intersecting P1 at point A.
+<Point Tool>Point at A.      ","['Circle Tool', 'Circle Tool', 'Point Tool']","[[], [], ['A'], []]",[]
+Alpha,https://euclidea.fandom.com/wiki/Inscribed_Square,"Description: Inscribe a square in the circle. One vertex of the square is given.Let O be the center of the circle and A the vertex.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line OA, intersecting the circle at point B.
+<Perpendicular Bisector Tool>Construct the perpendicular bisector of AB, intersecting the circle at points C and D.
+<Line Tool>Construct line AC.
+<Line Tool>Construct line BC.
+<Line Tool>Construct line BD.
+<Line Tool>Construct line AD.","['Line Tool', 'Perpendicular Bisector Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['O', 'A'], ['B', 'OA'], ['C', 'AB', 'D'], ['AC'], ['BC'], ['BD'], ['AD']]","['O', 'A']"
+Beta,https://euclidea.fandom.com/wiki/Angle_Bisector,"Description: Construct the line that bisects the given angle.Let A be the vertex of the angle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center A and an arbitrary radius, intersecting the sides of the angle at points B and C.
+<Perpendicular Bisector Tool>Construct the perpendicular bisector of BC.","['Circle Tool', 'Perpendicular Bisector Tool']","[['A'], ['B', 'C'], ['BC']]",['A']
+Beta,https://euclidea.fandom.com/wiki/Intersection_of_Angle_Bisectors,"Description: Construct the point where the angle bisectors of the triangle are intersected.Given the triangle ABC.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Angle Bisector Tool>Construct the angle bisector A1 of  angle BAC.
+<Angle Bisector Tool>Construct the angle bisector A2 of  angle ACB, intersecting A1 at D.","['Angle Bisector Tool', 'Angle Bisector Tool']","[['ABC'], ['BAC'], ['ACB', 'D']]",['ABC']
+Beta,https://euclidea.fandom.com/wiki/Angle_of_30%C2%B0,"Description: Construct an angle of 30° with the given side.Let A be the initial point of the given ray.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with an arbitrary center B and radius AB, intersecting the ray at point C. Although the image shown here places B on the ray, this construction works even when point B is not on the ray, so long as B is on the same half of the plane as the ray.
+<Circle Tool>Construct a circle with center C and radius BC, intersecting circle B at points D and E.
+<Line Tool>Construct line AD.","['Circle Tool', 'Circle Tool', 'Line Tool']","[['A'], ['AB', 'C', 'B'], ['BC', 'E', 'D'], ['AD']]",['A']
+Beta,https://euclidea.fandom.com/wiki/Double_Angle,"Description: Construct an angle equal to the given one so that they share one side.Let O be the vertex of the angle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with an arbitrary center A on one ray and an arbitrary radius so that it intersects the other ray at least once. Let B be one of those intersections.
+<Circle Tool>Construct a circle with another arbitrary center C on the first ray and radius BC, intersecting circle A at D.
+<Line Tool>Construct line OD.","['Circle Tool', 'Circle Tool', 'Line Tool']","[['O'], ['B', 'A'], ['C', 'BC', 'D'], ['OD']]",['O']
+Beta,https://euclidea.fandom.com/wiki/Cut_Rectangle,"Description: Construct a line through the given point that cuts the rectangle into two parts of equal area.Given the rectangle ABCD and the point O.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC, a diagonal of the rectangle
+<Line Tool>Construct line BD, the other diagonal, intersecting AC at E
+<Line Tool>Construct line OE","['Line Tool', 'Line Tool', 'Line Tool']","[['ABCD', 'O'], ['AC'], ['BD', 'E'], ['OE']]","['ABCD', 'O']"
+Beta,https://euclidea.fandom.com/wiki/Drop_a_Perpendicular,"Description: Drop a perpendicular from the point to the line.Let O be the point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a circle with center O and an arbitrary radius so that it intersects the line at two points A and B
+<Perpendicular Bisector Tool>Construct the perpendicular bisector of AB","['Line Tool', 'Perpendicular Bisector Tool']","[['O'], ['B', 'A'], ['AB']]",['O']
+Beta,https://euclidea.fandom.com/wiki/Erect_a_Perpendicular,"Description: Erect a perpendicular from the point on the line.Let O be the point, and A and B two arbitrary points on the line so that O is between them.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ",<Angle Bisector Tool>Construct the angle bisector of  angle AOB,['Angle Bisector Tool'],"[['O', 'A', 'B', 'O'], ['AOB']]","['O', 'A', 'B', 'O']"
+Beta,https://euclidea.fandom.com/wiki/Perpendicular_Tool,"Description: You have discovered the Perpendicular tool. Click on the line, then on the point.Let A be a line and B be a point, whether B is on or off line A (the level shows B off of A).
+Tool List: ['Perpendicular Tool']
+Solution: ","<Perpendicular Tool>With the perpendicular tool active, select the line, then the point.",['Perpendicular Tool'],"[['A', 'B', 'B', 'A', 'B', 'A'], []]","['A', 'B', 'B', 'A', 'B', 'A']"
+Beta,https://euclidea.fandom.com/wiki/Tangent_to_Circle_at_Point,"Description: Construct a tangent to the circle at the given point.Let O be the center of the circle and A the point on it.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line OA
+<Perpendicular Tool>Construct the perpendicular to the line OA from point A","['Line Tool', 'Perpendicular Tool']","[['O', 'A'], ['OA'], []]","['O', 'A']"
+Beta,https://euclidea.fandom.com/wiki/Circle_Tangent_to_Line,"Description: Construct a circle with the given center that is tangent to the given line.Let O be the center.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to the line from point O, intersecting the line at A
+<Circle Tool>Construct the circle with center O and radius OA","['Perpendicular Tool', 'Circle Tool']","[['O'], ['A'], ['OA']]",['O']
+Beta,https://euclidea.fandom.com/wiki/Circle_in_Rhombus,"Description: Inscribe a circle in the rhombus.Given the rhombus ABCD.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC, a diagonal of the rhombus
+<Line Tool>Construct line BD, the other diagonal of the rhombus, intersecting AC at O
+<Perpendicular Tool>Construct the perpendicular to AB through O, intersecting AB at E
+<Circle Tool>Construct the circle with center O radius OE","['Line Tool', 'Line Tool', 'Perpendicular Tool', 'Circle Tool']","[['ABCD'], ['AC'], ['BD', 'O'], ['E', 'AB'], ['OE']]",['ABCD']
+Gamma,https://euclidea.fandom.com/wiki/Chord_Midpoint,"Description: Construct a chord whose midpoint is given.Let A be the center and B the given midpoint.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB
+<Perpendicular Tool>Construct the perpendicular to AB through B","['Line Tool', 'Perpendicular Tool']","[['A', 'B'], ['AB'], []]","['A', 'B']"
+Gamma,https://euclidea.fandom.com/wiki/Triangle_by_Angle_and_Orthocenter,"Description: Construct a segment connecting the sides of the angle to get a triangle whose orthocenter is in the point O.Let A be the vertex of the angle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to one side R1 of the angle through O, intersecting the second side at A
+<Perpendicular Tool>Construct the perpendicular to the second side R2 of the angle through O, intersecting the first side at B
+<Line Tool>Construct line AB","['Perpendicular Tool', 'Perpendicular Tool', 'Line Tool']","[['O', 'A'], [], ['B'], ['AB']]","['O', 'A']"
+Gamma,https://euclidea.fandom.com/wiki/Intersection_of_Perpendicular_Bisectors,"Description: Construct a segment connecting the sides of the angle to get a triangle whose perpendicular bisectors are intersected in the point O.Let A be the vertex of the angle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the circle with center O and radius OA, intersecting the sides of the angle at B and C
+<Line Tool>Construct line BC","['Circle Tool', 'Line Tool']","[['O', 'A'], ['B', 'C', 'OA'], ['BC']]","['O', 'A']"
+Gamma,https://euclidea.fandom.com/wiki/Three_equal_segments_-_1,"Description: Given an angle ABC and a point M inside it, find points D on BA and E on BC and construct segments DM and ME such that BD = DM = ME.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of BM, intersecting AB at D
+<Circle Tool>Construct the circle with center M and radius DM, intersecting BC at E and F
+<Line Tool>Construct line DM
+<Line Tool>Construct line ME","['Perpendicular Tool', 'Circle Tool', 'Line Tool', 'Line Tool']","[['ABC', 'M', 'D', 'BA', 'E', 'BC', 'DM', 'ME', 'BD', 'DM', 'ME'], ['AB', 'BM'], ['F'], [], []]","['ABC', 'M', 'D', 'BA', 'E', 'BC', 'DM', 'ME', 'BD', 'DM', 'ME']"
+Gamma,https://euclidea.fandom.com/wiki/Circle_through_Point_Tangent_to_Line,"Description: Construct a circle through the point A that is tangent to the given line at the point B.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB
+<Perpendicular Tool>Construct the perpendicular to the line from B, intersecting the perpendicular bisector at O
+<Circle Tool>Construct the circle with center O and radius OA (or OB)","['Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool']","[['A', 'B'], ['AB'], ['O'], ['OB', 'OA']]","['A', 'B']"
+Gamma,https://euclidea.fandom.com/wiki/Midpoints_of_Trapezoid_Bases,"Description: Construct a line passing through the midpoints of the trapezoid bases.Given the trapezoid ABCD.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of the base AB, intersecting AB at E
+<Perpendicular Tool>Construct the perpendicular bisector of the base CD, intersecting CD at F
+<Line Tool>Construct line EF","['Perpendicular Tool', 'Perpendicular Tool', 'Line Tool']","[['ABCD'], ['AB', 'E'], ['F', 'CD'], ['EF']]",['ABCD']
+Gamma,https://euclidea.fandom.com/wiki/Angle_of_45%C2%B0,"Description: Construct an angle of 45° with the given side.Let A be the initial point of the given ray and B a distinct arbitrary point on that ray.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to the ray from A; let C be a distinct arbitrary point on that perpendicular
+<Angle Bisector Tool>Construct the angle bisector of  angle BAC","['Perpendicular Tool', 'Angle Bisector Tool']","[['A', 'B'], ['C'], ['BAC']]","['A', 'B']"
+Gamma,https://euclidea.fandom.com/wiki/Lozenge,"Description: Construct a rhombus with the given side and an angle of 45° in a vertex.Given the side AB (A on the left to match the orientation in explore mode)
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to AB from A; let C be a distinct arbitrary point on that perpendicular (above A, to match the orientation in explore mode)
+<Angle Bisector Tool>Construct the angle bisector of  angle BAC
+<Circle Tool>Construct the circle with center A and radius AB, intersecting the angle bisector at D and line AC at E with E on the side of A opposite from C
+<Perpendicular Tool>Construct the perpendicular to AC through D
+<Line Tool>Construct line BE","['Perpendicular Tool', 'Angle Bisector Tool', 'Circle Tool', 'Perpendicular Tool', 'Line Tool']","[['AB', 'A'], ['C'], ['BAC'], ['AC', 'E', 'D'], [], ['BE']]","['AB', 'A']"
+Gamma,https://euclidea.fandom.com/wiki/Center_of_Quadrilateral,"Description: Construct the midpoint of the segment that connects the midpoints of the diagonals of the quadrilateral.Given the quadrilateral ABCD (arbitrary which vertex is A)
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at E
+<Perpendicular Tool>Construct the perpendicular bisector of CD, intersecting CD at F
+<Perpendicular Tool>Construct the perpendicular bisector of EF
+<Line Tool>Construct line EF
+<Perpendicular Tool>Point at the intersection of EF and its perpendicular bisector","['Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Line Tool', 'Perpendicular Tool']","[['ABCD', 'A'], ['AB', 'E'], ['F', 'CD'], ['EF'], [], []]","['ABCD', 'A']"
+Delta,https://euclidea.fandom.com/wiki/Double_Segment,"Description: Construct a point C on the line AB such that |AC|=2|AB| using only a compass.
+Tool List: ['Point Tool', 'Circle Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the circle with center A and radius AB
+<Circle Tool>Construct the circle with center B and radius AB, intersecting circle A at D and E
+<Circle Tool>Construct the circle with center D and radius DE, intersecting circle B at C
+<Point Tool>Point at C","['Circle Tool', 'Circle Tool', 'Circle Tool', 'Point Tool']","[['C', 'AB', 'AC', 'AB'], ['A'], ['E', 'D', 'B'], ['DE'], []]","['C', 'AB', 'AC', 'AB']"
+Delta,https://euclidea.fandom.com/wiki/Angle_of_60%C2%B0_-_2,"Description: Construct a straight line through the given point that makes an angle of 60° with the given line.Let A be the given point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle B with radius AB, intersecting the line at point C
+<Circle Tool>Construct circle C with radius AC, intersecting circle B at point D
+<Circle Tool>Construct circle D with radius CD, intersecting circle C at points E and F (E on the left to match the orientation in explore mode)
+<Line Tool>Construct line AE","['Circle Tool', 'Circle Tool', 'Circle Tool', 'Line Tool']","[['A'], ['AB', 'C', 'B'], ['D', 'AC'], ['F', 'E', 'CD'], ['AE']]",['A']
+Delta,https://euclidea.fandom.com/wiki/Circumscribed_Equilateral_Triangle,"Description: Construct an equilateral triangle that is circumscribed about the circle and contains the given point.Let O be the center of the circle and A the point on it.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line OA, intersecting the circle at B
+<Perpendicular Tool>Construct the perpendicular to OA from A
+<Circle Tool>Construct the circle with center B and radius OB, intersecting the circle at C and D, and line OA at E
+<Line Tool>Construct line CE
+<Line Tool>Construct line DE","['Line Tool', 'Perpendicular Tool', 'Circle Tool', 'Line Tool', 'Line Tool']","[['O', 'A'], ['B', 'OA'], [], ['C', 'OB', 'E', 'D'], ['CE'], ['DE']]","['O', 'A']"
+Delta,https://euclidea.fandom.com/wiki/Equilateral_Triangle_in_Circle,"Description: Inscribe an equilateral triangle in the circle using the given point as a vertex. The center of the circle is not given.Let A be the vertex.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center A and an arbitrary radius, intersecting the original circle at B and C
+<Circle Tool>Construct the circle with center B and radius AB, intersecting circle A at D and E
+<Perpendicular Tool>Construct the perpendicular bisector of CD, intersecting the original circle at F
+<Perpendicular Tool>Construct the perpendicular bisector of CE, intersecting the original circle at G
+<Line Tool>Construct line FG (total 9E)","['Circle Tool', 'Circle Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Line Tool']","[['A'], ['B', 'C'], ['AB', 'D', 'E'], ['F', 'CD'], ['G', 'CE'], ['FG']]",['A']
+Delta,https://euclidea.fandom.com/wiki/Cut_Two_Rectangles,"Description: Construct a line that cuts each of the rectangles into two parts of equal area.Given the rectangles ABCD and EFGH.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC, a diagonal of the first rectangle
+<Line Tool>Construct line BD, the other diagonal, intersecting the previous diagonal at I
+<Line Tool>Construct line EG, a diagonal of the second rectangle
+<Line Tool>Construct line FH, the other diagonal, intersecting the previous diagonal at J
+<Line Tool>Construct line IJ","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['ABCD', 'EFGH'], ['AC'], ['BD', 'I'], ['EG'], ['FH', 'J'], ['IJ']]","['ABCD', 'EFGH']"
+Delta,https://euclidea.fandom.com/wiki/Square_Root_of_2,"Description: Let |AB|=1. Construct a point C on the ray AB such that the length of AC is equal to √2.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to AB from B
+<Circle Tool>Construct the circle with center B and radius AB, intersecting the perpendicular at D
+<Circle Tool>Construct the circle with center A and radius AD, intersecting the ray at C
+<Point Tool>Point at C","['Perpendicular Tool', 'Circle Tool', 'Circle Tool', 'Point Tool']","[['AB', 'C', 'AB', 'AC'], ['B'], ['D'], ['AD', 'A'], []]","['AB', 'C', 'AB', 'AC']"
+Delta,https://euclidea.fandom.com/wiki/Square_Root_of_3,"Description: Let |AB|=1. Construct a point C on the ray AB such that the length of AC is equal to √3.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the circle with center B and radius AB, intersecting the ray at D
+<Circle Tool>Construct the circle with center D and radius BD, intersecting circle B at E
+<Circle Tool>Construct the circle with center A and radius AE, intersecting the ray at C
+<Point Tool>Point at C","['Circle Tool', 'Circle Tool', 'Circle Tool', 'Point Tool']","[['AB', 'C', 'AB', 'AC'], ['B', 'D'], ['BD', 'E'], ['AE', 'A'], []]","['AB', 'C', 'AB', 'AC']"
+Delta,https://euclidea.fandom.com/wiki/Angle_of_15%C2%B0,"Description: Construct an angle of 15° with the given side.Let A be the initial point of the given ray.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with an arbitrary center B and radius AB, intersecting the ray at C
+<Circle Tool>Construct the circle with center C and radius BC, intersecting circle B at D and E (D above ray to match orientation of explore mode)
+<Angle Bisector Tool>Construct the angle bisector of  angle DAC","['Circle Tool', 'Circle Tool', 'Angle Bisector Tool']","[['A'], ['AB', 'C', 'B'], ['BC', 'E', 'D'], ['DAC']]",['A']
+Delta,https://euclidea.fandom.com/wiki/Square_by_Opposite_Midpoints,"Description: Construct a square, given two midpoints of opposite sides.Let A and B be the given midpoints.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the circle with center A and radius AB
+<Circle Tool>Construct the circle with center B and radius AB, intersecting circle A at C and D.
+<Circle Tool>Construct the circle with center C and radius CB
+<Line Tool>We draw the line (AC) that crosses the circle of center C in D.","['Circle Tool', 'Circle Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['AB'], ['C', 'D'], ['CB'], ['AC']]","['A', 'B']"
+Delta,https://euclidea.fandom.com/wiki/Square_by_Adjacent_Midpoints,"Description: Construct a square, given two midpoints of adjacent sides.Let A and B be the given midpoints.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB
+<Perpendicular Tool>Construct the perpendicular to AB from A
+<Perpendicular Tool>Construct the angle bisector of  angle BAC with C an arbitrary point on the perpendicular (to match the orientation of explore mode, choose C above A)
+<Perpendicular Tool>Construct the perpendicular to that angle bisector through B, intersecting AC at D
+<Circle Tool>Construct the circle with center B and radius BD, intersecting BD at E and AC at F
+<Perpendicular Tool>Construct the perpendicular bisector of BE
+<Perpendicular Tool>Construct the perpendicular to the angle bisector of  angle BAC through F","['Line Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool', 'Perpendicular Tool', 'Perpendicular Tool']","[['A', 'B'], ['AB'], [], ['BAC', 'C'], ['D', 'AC'], ['F', 'BD', 'E'], ['BE'], []]","['A', 'B']"
+Epsilon,https://euclidea.fandom.com/wiki/Parallel_Line,"Description: Construct a line parallel to the given line and through the given point.Let A be the given point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to the line through A
+<Perpendicular Tool>Construct the perpendicular to the previous perpendicular from A","['Perpendicular Tool', 'Perpendicular Tool']","[['A'], [], []]",['A']
+Epsilon,https://euclidea.fandom.com/wiki/Parallel_Tool,"Description: You have discovered the Parallel tool. Click on the line, then on the point.
+Tool List: ['Parallel Tool']
+Solution: ","<Parallel Tool>With the parallel tool active, click on the line then on the point.",['Parallel Tool'],"[[], []]",[]
+Epsilon,https://euclidea.fandom.com/wiki/Parallelogram_by_Three_Vertices,"Description: Construct a parallelogram whose three of four vertices are given.Let A, B and C be the given vertices (to match the orientation of explore mode, place A on top and B on the left)
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB
+<Line Tool>Construct line BC
+<Parallel Tool>Construct the parallel to AB through C
+<Parallel Tool>Construct the parallel to BC through A","['Line Tool', 'Line Tool', 'Parallel Tool', 'Parallel Tool']","[['A', 'B', 'C', 'A', 'B'], ['AB'], ['BC'], [], []]","['A', 'B', 'C', 'A', 'B']"
+Epsilon,https://euclidea.fandom.com/wiki/Line_Equidistant_from_Two_Points_-_1,"Description: Construct a line through the point C and at equal distance from the points A and B but that does not pass between them.Given points A, B, and C (C already labeled, choice of A and B is arbitrary):
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB
+<Parallel Tool>Construct the parallel to AB through C","['Line Tool', 'Parallel Tool']","[['C', 'A', 'B', 'A', 'B', 'C', 'C', 'A', 'B'], ['AB'], []]","['C', 'A', 'B', 'A', 'B', 'C', 'C', 'A', 'B']"
+Epsilon,https://euclidea.fandom.com/wiki/Line_Equidistant_from_Two_Points_-_2,"Description: Construct a line through the point C that goes between the points A and B and that is at equal distance from them.Given points A, B, and C, with C labeled and the choice of A and B arbitrary:
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB
+<Line Tool>Construct line AB, intersecting its perpendicular bisector at D
+<Line Tool>Construct line CD","['Perpendicular Tool', 'Line Tool', 'Line Tool']","[['C', 'A', 'B', 'A', 'B', 'C', 'C', 'A', 'B'], ['AB'], ['D'], ['CD']]","['C', 'A', 'B', 'A', 'B', 'C', 'C', 'A', 'B']"
+Epsilon,https://euclidea.fandom.com/wiki/Hash,"Description: Construct a line through the given point on which two pairs of parallel lines cut off equal line segments.Let O be the given point, and ABCD the parallelogram created by the two pairs of parallel lines (A on top to match the orientation of explore mode):
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC, a diagonal of the parallelogram
+<Parallel Tool>Construct the parallel to AC through O","['Line Tool', 'Parallel Tool']","[['O', 'ABCD', 'A'], ['AC'], []]","['O', 'ABCD', 'A']"
+Epsilon,https://euclidea.fandom.com/wiki/Shift_Angle,"Description: Construct an angle from the given point that is equal to the given angle so that their sides are parallel.Let O be the given point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Angle Bisector Tool>Construct the parallel to one side of the angle through O
+<Angle Bisector Tool>Construct the parallel to the other side of the angle through O","['Angle Bisector Tool', 'Angle Bisector Tool']","[['O'], [], []]",['O']
+Epsilon,https://euclidea.fandom.com/wiki/Line_Equidistant_from_Two_Lines,"Description: Construct a straight line parallel to the given parallel lines that lies at equal distance from them.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to one line from an arbitrary point A on it, intersecting the other line at B
+<Perpendicular Tool>Construct the perpendicular bisector of AB","['Perpendicular Tool', 'Perpendicular Tool']","[[], ['B', 'A'], ['AB']]",[]
+Epsilon,https://euclidea.fandom.com/wiki/Circumscribed_Square,"Description: Circumscribe a square about the circle. Two of its sides should be parallel to the given line.Let O be the center of the given circle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to the line through O, intersecting the circle at A and B
+<Perpendicular Tool>Construct the perpendicular to AB from A
+<Perpendicular Tool>Construct the perpendicular to AB from B
+<Circle Tool>Construct the circle with center A and radius OA, intersecting the perpendicular to AB from A at C and D
+<Perpendicular Tool>Construct the perpendicular to CD from C
+<Perpendicular Tool>Construct the perpendicular to CD from D (total 16E)","['Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool', 'Perpendicular Tool', 'Perpendicular Tool']","[['O'], ['B', 'A'], ['AB'], [], ['C', 'D', 'OA'], ['CD'], []]",['O']
+Epsilon,https://euclidea.fandom.com/wiki/Square_in_Square,"Description: Inscribe a square in the square. A vertex is given.Given the square ABCD and E the given vertex.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the circle with center A and radius AE, intersecting AD at F
+<Perpendicular Tool>Construct the perpendicular to AD through F, intersecting BC at G
+<Line Tool>Construct line EG
+<Perpendicular Tool>Construct the perpendicular to EG from E, intersecting AD at H
+<Perpendicular Tool>Construct the perpendicular to EG from G, intersecting CD at I
+<Line Tool>Construct the line HI (total 12E)","['Circle Tool', 'Perpendicular Tool', 'Line Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Line Tool']","[['A', 'ABCD', 'E'], ['F', 'AD', 'AE'], ['G', 'BC'], ['EG'], ['H'], ['I', 'CD'], ['HI']]","['A', 'ABCD', 'E']"
+Epsilon,https://euclidea.fandom.com/wiki/Circle_Tangent_to_Square_Side,"Description: Construct a circle that is tangent to a side of the square and goes through the vertices of the opposite side.Given the square ABCD (AB on the bottom for the solution to match the hint mode orientation)
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting CD at E and AB at F
+<Perpendicular Tool>Construct the perpendicular bisector of AE, intersecting EF at G
+<Circle Tool>Construct the circle with center G and radius AG (or EG)","['Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool']","[['ABCD', 'AB'], ['F', 'E', 'CD'], ['EF', 'G', 'AE'], ['AG', 'EG']]","['ABCD', 'AB']"
+Epsilon,https://euclidea.fandom.com/wiki/Regular_Hexagon,"Description: Construct a regular hexagon with the given side.Given the side AB.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct the circle with center A and radius AB
+<Circle Tool>Construct the circle with center B and radius AB, intersecting circle A at C and D (C below AB to match the orientation of explore mode)
+<Line Tool>Construct line AC, intersecting circle A at E
+<Line Tool>Construct line BC, intersecting circle B at F
+<Parallel Tool>Construct the parallel to AC through F
+<Parallel Tool>Construct the parallel to BC through E, intersecting the the parallel to AC at G
+<Perpendicular Tool>Construct the perpendicular bisector of DG (total 15E)","['Circle Tool', 'Circle Tool', 'Line Tool', 'Line Tool', 'Parallel Tool', 'Parallel Tool', 'Perpendicular Tool']","[['AB'], ['A'], ['C', 'B', 'D'], ['E', 'AC'], ['F', 'BC'], [], ['G'], ['DG']]",['AB']
+Zeta,https://euclidea.fandom.com/wiki/Point_Reflection,"Description: Reflect the segment across the point.Given the segment AB and O the point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AO
+<Circle Tool>Construct the circle with center O and radius AO, intersecting AO at C
+<Parallel Tool>Construct the parallel to AB through C
+<Line Tool>Construct line BO, intersecting the parallel to AB at D
+<Point Tool>Point at D","['Line Tool', 'Circle Tool', 'Parallel Tool', 'Line Tool', 'Point Tool']","[['AB', 'O'], ['AO'], ['C'], [], ['BO', 'D'], []]","['AB', 'O']"
+Zeta,https://euclidea.fandom.com/wiki/Reflection,"Description: Reflect the segment across the line.Given the segment AB.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a circle with an arbitrary center C on the line and radius AC
+<Line Tool>Construct a circle with another arbitrary center D on the line and radius AD, intersecting circle C at E
+<Line Tool>Construct a circle with an arbitrary center F on the line and radius BF
+<Line Tool>Construct a circle with another arbitrary center G on the line and radius BG, intersecting circle F at H
+<Line Tool>Construct line EH","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['AB'], ['C', 'AC'], ['AD', 'E', 'D'], ['F', 'BF'], ['H', 'G', 'BG'], ['EH']]",['AB']
+Zeta,https://euclidea.fandom.com/wiki/Copy_Segment,"Description: Construct a segment from the given point that is equal to the given segment and lies on the same line with it.Given the segment AB and the point C.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC
+<Perpendicular Tool>Construct the perpendicular bisector of AC, intersecting AC at D
+<Circle Tool>Construct the circle with center D and radius BD, intersecting AC at E
+<Point Tool>Point at E","['Line Tool', 'Perpendicular Tool', 'Circle Tool', 'Point Tool']","[['AB', 'C'], ['AC'], ['D'], ['BD', 'E'], []]","['AB', 'C']"
+Zeta,https://euclidea.fandom.com/wiki/Given_Angle_Bisector,"Description: Construct two straight lines through the two given points respectively so that the given line is a bisector of the angle that they make.Let A and B be the given points.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a circle with an arbitrary center C on the line and radius AC
+<Line Tool>Construct a circle with another arbitrary center D on the line and radius AD, intersecting circle C at E
+<Line Tool>Construct line BE, intersecting the line at F
+<Line Tool>Construct line AF","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['A', 'B'], ['C', 'AC'], ['AD', 'E', 'D'], ['BE', 'F'], ['AF']]","['A', 'B']"
+Zeta,https://euclidea.fandom.com/wiki/Non-collapsing_Compass,"Description: Construct a circle with the given center and the radius equal to the length of the given segment.Given the segment AB and the point C.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of A and C.
+<Perpendicular Tool>Construct the circle with center arbitrary point D on the perpendicular bisector of A and C and with radius DB.
+<Perpendicular Tool>Construct the circle with center arbitrary point E on the perpendicular bisector of A and C and with radius EB, intersecting circle D at F.
+<Circle Tool>Construct the circle with center C and radius CF. (6E)","['Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool']","[['AB', 'C'], ['A'], ['DB', 'D'], ['F', 'EB', 'E'], ['CF']]","['AB', 'C']"
+Zeta,https://euclidea.fandom.com/wiki/Compass_Tool,"Description: You have discovered the Non-collapsing Compass tool. Click on two points to set the radius length, then on the center of the circle.
+Tool List: ['Compass Tool']
+Solution: ","<Compass Tool>With the compass tool active, click on one endpoint of the segment, then another endpoint of the segment, then on the destination point.",['Compass Tool'],"[[], []]",[]
+Zeta,https://euclidea.fandom.com/wiki/Translate_Segment,"Description: Construct a segment from the given point parallel and equal to the given segment.Given the segment AB and the point C.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Use the non-collapsing compass to construct the circle with radius AB and center C
+<Parallel Tool>Construct the parallel to AB through C, intersecting the circle at two points
+<Line Tool>Use the intersect tool on the circle and parallel line to select both points at once","['Circle Tool', 'Parallel Tool', 'Line Tool']","[['AB', 'C'], [], [], []]","['AB', 'C']"
+Zeta,https://euclidea.fandom.com/wiki/Triangle_by_Three_Sides,"Description: Construct a triangle with the side AB and the two other sides equal to the given segments.Given the other segments CD and EF.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Use the non-collapsing compass to construct the circle with radius CD and center A
+<Circle Tool>Use the non-collapsing compass to construct the circle with radius EF and center B, intersecting circle A at G and H
+<Line Tool>Construct line AG
+<Line Tool>Construct line BG","['Circle Tool', 'Circle Tool', 'Line Tool', 'Line Tool']","[['AB', 'CD', 'EF'], ['A'], ['H', 'G', 'B'], ['AG'], ['BG']]","['AB', 'CD', 'EF']"
+Zeta,https://euclidea.fandom.com/wiki/Parallelogram,"Description: Construct a parallelogram with the given side and the midpoint of the opposite side in the given point.Given the segment AB and the point C.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at D
+<Circle Tool>Use the non-collapsing compass to construct the circle with radius AD and center C
+<Parallel Tool>Construct the parallel to AB through C, intersecting circle C at E and F
+<Line Tool>Construct line AE
+<Line Tool>Construct line BF","['Perpendicular Tool', 'Circle Tool', 'Parallel Tool', 'Line Tool', 'Line Tool']","[['AB', 'C'], ['D'], ['AD'], ['F', 'E'], ['AE'], ['BF']]","['AB', 'C']"
+Zeta,https://euclidea.fandom.com/wiki/Nine_Point_Circle,"Description: Construct a circle that passes through the midpoints of sides of the given acute triangle.Given the triangle ABC.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to AB through C, intersecting AB at D
+<Perpendicular Tool>Construct the perpendicular to BC through A, intersecting BC at E
+<Perpendicular Tool>Construct the perpendicular bisector of DE, intersecting AC at F
+<Perpendicular Tool>Construct the perpendicular bisector of DF, intersecting the perpendicular bisector of DE at G
+<Circle Tool>Construct the circle with center G and radius DG","['Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool']","[['ABC'], ['C', 'AB', 'D'], ['BC', 'E', 'A'], ['F', 'DE', 'AC'], ['G', 'DF'], ['DG']]",['ABC']
+Zeta,https://euclidea.fandom.com/wiki/Symmetry_of_Four_Lines,"Description: Three lines are intersected in a point. Construct a line so that the set of all 4 lines is mirror symmetric.Let O be the intersection of the three lines.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center O and an arbitrary radius, intersecting the lines at six points; let A, B and C be a set of three consecutive points
+<Circle Tool>Use the non-collapsing compass to construct the circle with radius AB and center C, intersecting circle O at D and E
+<Line Tool>Construct line OD","['Circle Tool', 'Circle Tool', 'Line Tool']","[['O'], ['B', 'C', 'A'], ['E', 'D', 'AB'], ['OD']]",['O']
+Zeta,https://euclidea.fandom.com/wiki/Parallelogram_by_Three_Midpoints,"Description: Construct a parallelogram given three of the midpoints.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Use the non-collapsing compass to construct the circle with radius AC and center B
+<Circle Tool>Use the non-collapsing compass to construct the circle with radius BC and center A, intersecting circle B at D and E, with D on the opposite side of C from AB
+<Line Tool>Construct line CD
+<Parallel Tool>Construct the parallel to CD through A
+<Parallel Tool>Construct the parallel to CD through B
+<Line Tool>Construct line CE, intersecting circle A at F and circle B at G
+<Parallel Tool>Construct the parallel to CE through D","['Circle Tool', 'Circle Tool', 'Line Tool', 'Parallel Tool', 'Parallel Tool', 'Line Tool', 'Parallel Tool']","[[], ['AC', 'B'], ['E', 'D', 'AB', 'C', 'BC', 'A'], ['CD'], [], [], ['F', 'G', 'CE'], []]",[]
+Eta,https://euclidea.fandom.com/wiki/Sum_of_Areas_of_Squares,"Description: Construct a square whose area equals the sum of the areas of the two given squares and all three have the common angle.Let O be the common vertex of the squares, A the second vertex of one square on one line and B the second vertex of the other square on the other line.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Use the non-collapsing compass to construct the circle with radius AB and center O, intersecting one line at C and the other line at D
+<Perpendicular Tool>Construct the perpendicular to OC from C
+<Perpendicular Tool>Construct the perpendicular to OD from D","['Circle Tool', 'Perpendicular Tool', 'Perpendicular Tool']","[['O', 'A', 'B'], ['C', 'AB', 'D'], ['OC'], ['OD']]","['O', 'A', 'B']"
+Eta,https://euclidea.fandom.com/wiki/Annulus,"Description: Construct a circle that is concentric with the given one and divides it into 2 parts of equal area.Let O be the center.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct an arbitrary line through O, intersecting the circle at A
+<Perpendicular Tool>Construct the perpendicular bisector of OA, intersecting at B
+<Circle Tool>Construct the circle with center B and radius OB, intersecting the bisector at C
+<Circle Tool>Construct the circle with center O and radius OC","['Line Tool', 'Perpendicular Tool', 'Circle Tool', 'Circle Tool']","[['O'], ['A'], ['B', 'OA'], ['OB', 'C'], ['OC']]",['O']
+Eta,https://euclidea.fandom.com/wiki/Angle_of_75%C2%B0,"Description: Construct an angle of 75° with the given side.Let A be the initial point of the given ray.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with an arbitrary center B not on the ray and radius AB, so that it intersects the ray at C and AC<AB
+<Circle Tool>Construct the circle with center C and radius BC, intersecting circle B at D
+<Angle Bisector Tool>Construct the angle bisector of  angle CAD","['Circle Tool', 'Circle Tool', 'Angle Bisector Tool']","[['A'], ['AC', 'AB', 'C', 'B'], ['BC', 'D'], ['CAD']]",['A']
+Eta,https://euclidea.fandom.com/wiki/Line_Equidistant_from_Three_Points,"Description: Construct a line that is at equal distance from the given three points.Let A, B and C be the given points.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB
+<Perpendicular Tool>Construct the perpendicular to AB through C, intersecting AB at D
+<Perpendicular Tool>Construct the perpendicular bisector of CD","['Line Tool', 'Perpendicular Tool', 'Perpendicular Tool']","[['A', 'B', 'C'], ['AB'], ['D'], ['CD']]","['A', 'B', 'C']"
+Eta,https://euclidea.fandom.com/wiki/Heron%27s_Problem,"Description: Construct a point C on the given line and segments AC and BC such that the sum of their length is minimal.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a circle with an arbitrary center D on the line and radius AD
+<Line Tool>Construct a circle with an arbitrary center E on the line and radius AE, intersecting circle D at F
+<Line Tool>Construct line BF, intersecting the line at C
+<Line Tool>Construct line AC","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['C', 'AC', 'BC'], ['AD', 'D'], ['F', 'AE', 'E'], ['BF'], []]","['C', 'AC', 'BC']"
+Eta,https://euclidea.fandom.com/wiki/Circumscribed_Circle,"Description: Construct the circumcircle of the triangle.Given the triangle ABC
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB
+<Perpendicular Tool>Construct the perpendicular bisector of BC, intersecting the perpendicular bisector of AB at D
+<Circle Tool>Construct the circle with center D and radius AD","['Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool']","[['ABC'], ['AB'], ['BC', 'D'], ['AD']]",['ABC']
+Eta,https://euclidea.fandom.com/wiki/Inscribed_Circle,"Description: Construct the incircle of the triangle.Given the triangle ABC
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Angle Bisector Tool>Construct the angle bisector of  angle CAB
+<Angle Bisector Tool>Construct the angle bisector of  angle ABC, intersecting the angle bisector of  angle CAB at D
+<Perpendicular Tool>Construct the perpendicular to AB through D, intersecting AB at E
+<Circle Tool>Construct the circle with center D and radius DE","['Angle Bisector Tool', 'Angle Bisector Tool', 'Perpendicular Tool', 'Circle Tool']","[['ABC'], ['CAB'], ['D'], ['AB', 'E'], ['DE']]",['ABC']
+Eta,https://euclidea.fandom.com/wiki/Circle_Tangent_to_Three_Lines,"Description: Construct a circle that is tangent to the three given lines. Two of the lines are parallel.Given the intersections of the lines A and B.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Angle Bisector Tool>Construct the angle bisector of  angle CAB, with C an arbitrary point on one of the parallel lines.
+<Angle Bisector Tool>Construct the angle bisector of  angle ABD, with D an arbitrary point on the other parallel line and on the same side as C from the third given line, intersecting the angle bisector of  angle CAB at E
+<Perpendicular Tool>Construct the perpendicular to AB through E, intersecting AB at F
+<Circle Tool>Construct the circle with center E and radius EF","['Angle Bisector Tool', 'Angle Bisector Tool', 'Perpendicular Tool', 'Circle Tool']","[['A', 'B'], ['CAB', 'C'], ['E', 'D', 'ABD'], ['F', 'AB'], ['EF']]","['A', 'B']"
+Eta,https://euclidea.fandom.com/wiki/Segment_by_Midpoint,"Description: Construct a segment with the ends on the sides of the angle such that the given point is its midpoint.Let A be the vertex of the angle and B the midpoint.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Parallel Tool>Construct parallel of one ray through B, intersecting the other ray at C
+<Circle Tool>Construct the circle with center C and radius AC, intersecting AC at D
+<Line Tool>Construct line BD","['Parallel Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['C'], ['D', 'AC'], ['BD']]","['A', 'B']"
+Eta,https://euclidea.fandom.com/wiki/Angle_Isosceles,"Description: Construct a line through the given point such that it cuts off equal segments on the sides of the angle.Let A be the vertex of the angle and B the point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Angle Bisector Tool>Construct the angle bisector A1 of the given angle
+<Perpendicular Tool>Construct the perpendicular to A1 through B","['Angle Bisector Tool', 'Perpendicular Tool']","[['A', 'B'], [], []]","['A', 'B']"
+Eta,https://euclidea.fandom.com/wiki/Excircle,"Description: Construct the excircle of the triangle formed by the three given lines.Let A, B and C be the intersections of the lines.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Angle Bisector Tool>Construct the angle bisector A1 of  angle DAB, with D an arbitrary point on the line that intersects AB at A
+<Angle Bisector Tool>Construct the angle bisector A2 of  angle EBA, with E an arbitrary point on the line that intersects AB at B, intersecting A1 at F
+<Perpendicular Tool>Construct the perpendicular to AB through F, intersecting AB at G
+<Circle Tool>Construct the circle with center F and radius FG","['Angle Bisector Tool', 'Angle Bisector Tool', 'Perpendicular Tool', 'Circle Tool']","[['A', 'B', 'C'], ['DAB', 'AB', 'D'], ['F', 'EBA', 'E'], ['G'], ['FG']]","['A', 'B', 'C']"
+Theta,https://euclidea.fandom.com/wiki/Perimeter_Bisector,"Description: Construct a straight line through a vertex of the triangle that divides its perimeter in half.Let A, B, and C be the vertices of the triangle
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a circle with center A and radius BC intersecting line AC at D
+<Line Tool>Construct a circle with center C and radius AB intersecting line AC at E
+<Perpendicular Tool>Construct the perpendicular bisector of DE intersecting line AC at F
+<Line Tool>Construct the line BF","['Line Tool', 'Line Tool', 'Perpendicular Tool', 'Line Tool']","[['A', 'B', 'C'], ['AC', 'BC', 'D'], ['AB', 'E'], ['F', 'DE'], ['BF']]","['A', 'B', 'C']"
+Theta,https://euclidea.fandom.com/wiki/Angle_54%C2%B0_Trisection,"Description: Construct two rays that divide the given angle of 54° into three equal parts.Let A be the vertex.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a circle with center B on either line and radius AB. Circle B intersects with line AB at point C, and the other line at point D.
+<Circle Tool>Construct a circle with center D and radius AD. Circle D intersects with circle B at point E.
+<Line Tool>Draw line AE, the first angle trisector.
+<Angle Bisector Tool>Bisect angle DAE, the second angle trisector.","['Line Tool', 'Circle Tool', 'Line Tool', 'Angle Bisector Tool']","[['A'], ['D', 'AB', 'C', 'B'], ['AD', 'E'], ['AE'], ['DAE']]",['A']
+Theta,https://euclidea.fandom.com/wiki/Interior_Angles,"Description: Construct a line through the point that crosses the two lines so that the interior angles are equal.Let A be the point of intersection between the two lines.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Point Tool> Let B be an arbitrary point on one of the lines, and C an arbitrary point on the other. Let O be the given point.
+<Angle Bisector Tool>Bisect the angle BAC. The new line contains an arbitrary point D.
+<Perpendicular Tool>Construct the line perpendicular to AD through O.","['Point Tool', 'Angle Bisector Tool', 'Perpendicular Tool']","[['A'], ['B', 'C', 'O'], ['BAC', 'D'], ['AD']]",['A']
+Theta,https://euclidea.fandom.com/wiki/Regular_Octagon,"Description: Construct a regular octagon with the given side.Let point A and point B be the two given points.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular to line AB through point A. Let point C be an arbitrary point on this new line (C below AB to match orientation of explore mode).
+<Line Tool>Construct the angle bisector of BAC. Let point D be an arbitrary point on this line.
+<Perpendicular Tool>Construct the perpendicular to line AD through point B. Let point E be an arbitrary point on this line on the opposite side of point B from point C.
+<Line Tool>Construct the angle bisector of ABE. This line intersects with line AD at point F and line AC at point G.
+<Perpendicular Tool>Construct the perpendicular to line AB through point F.
+<Perpendicular Tool>Construct the perpendicular to line AG through point G. This line intersects with line BE at point H.
+<Perpendicular Tool>Construct the perpendicular bisector of point B and point H. This line intersects with line BG at point I.
+<Perpendicular Tool>Construct the perpendicular of line AB through point I.
+<Perpendicular Tool>Construct the perpendicular of line AD through point G (total 29E).","['Perpendicular Tool', 'Line Tool', 'Perpendicular Tool', 'Line Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool']","[['A', 'B'], ['AB', 'C'], ['BAC', 'D'], ['AD', 'E'], ['F', 'G', 'AC', 'ABE'], [], ['BE', 'H', 'AG'], ['I', 'BG'], [], []]","['A', 'B']"
+Theta,https://euclidea.fandom.com/wiki/Triangle_Cleaver,"Description: Construct a line through the midpoint of a side of the triangle that bisects its perimeter.Let A, B, and C be the vertices of the triangle
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AC intersecting line AC at midpoint D
+<Line Tool>Construct the line BE that bisects the angle ABC
+<Line Tool>Draw the line parallel to BE that intersects D","['Perpendicular Tool', 'Line Tool', 'Line Tool']","[['A', 'B', 'C'], ['AC', 'D'], ['BE', 'ABC'], []]","['A', 'B', 'C']"
+Theta,https://euclidea.fandom.com/wiki/Torricelli_Point,"Description: Construct a point from which each side subtends an angle of 120 or 60.Let A, B, and C be the vertices of the triangle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle A with center A and radius AB.
+<Circle Tool>Construct circle B with center B and radius BA, intersecting circle A at D.
+<Line Tool>Construct line CD, intersecting circle B at E.
+<Perpendicular Tool>Construct line A as the perpendicular bisector of AE, intersecting line CD at F
+<Point Tool>Select point F using the point tool.","['Circle Tool', 'Circle Tool', 'Line Tool', 'Perpendicular Tool', 'Point Tool']","[['A', 'B', 'C'], ['AB'], ['D', 'BA'], ['E', 'CD'], ['F', 'AE'], []]","['A', 'B', 'C']"
+Theta,https://euclidea.fandom.com/wiki/Circle_Equidistant_from_Four_Points,"Description: Construct a circle equidistant from the given four points so that exactly two of them lie inside the circle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB
+<Perpendicular Tool>Construct the perpendicular bisector of CD intersecting the previous line at E
+<Line Tool>Construct the line AE
+<Circle Tool>Construct a circle with center E and radius EC, intersecting AE at F
+<Perpendicular Tool>Construct the perpendicular bisector of AF, intersecting AE at G
+<Circle Tool>Construct a circle with center E and radius EG","['Perpendicular Tool', 'Perpendicular Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Tool', 'Circle Tool']","[[], ['AB'], ['E', 'CD'], ['AE'], ['F', 'EC'], ['G', 'AF'], ['EG']]",[]
+Iota,https://euclidea.fandom.com/wiki/Minimum_Perimeter_-_1,"Description: Construct a triangle whose perimeter is the minimum possible whose vertices lie on the two sides of the angle and the third vertex is in the point A.Let O be the vertex of the angle and A the given point. Let B, C be abitary points on each ray, such that AB is bigger than AO and  AC is bigger than AO.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle O with center O and radius OA.
+<Circle Tool>Construct circle B with center B and radius BA, intersecting circle O at F.
+<Circle Tool>Construct circle B with center C and radius CA, intersecting circle O at G.
+<Line Tool>Construct line FG, intersecting line OB at H, intersecting line OC at I.
+<Line Tool>Construct line AH.
+<Line Tool>Construct line AI.","['Circle Tool', 'Circle Tool', 'Circle Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['A', 'O', 'A', 'B', 'C', 'AB', 'AO', 'AC', 'AO'], ['OA'], ['F', 'BA'], ['G', 'CA'], ['OB', 'OC', 'FG', 'H', 'I'], ['AH'], ['AI']]","['A', 'O', 'A', 'B', 'C', 'AB', 'AO', 'AC', 'AO']"
+Iota,https://euclidea.fandom.com/wiki/Third_Proportional,"Description: Construct a point D on the ray such that the segment AD is the third proportional to the given line segments.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle A with center A and radius AB.
+<Circle Tool>Construct circle C with center C and radius CA, intersecting circle A at E.
+<Circle Tool>Construct circle E with center E and radius EA, intersecting circle O at D.","['Circle Tool', 'Circle Tool', 'Circle Tool']","[['D', 'AD'], ['AB', 'A'], ['CA', 'E', 'C'], ['EA', 'O']]","['D', 'AD']"
+Iota,https://euclidea.fandom.com/wiki/Harmonic_Mean_of_Trapezoid_Bases,"Description: Join the legs of the trapezoid with a segment that is parallel to the bases and whose length is equal to the harmonic mean of their length.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC.
+<Line Tool>Construct line BD, intersecting line AC at E.
+<Line Tool>Construct line parallel to AB through E.","['Line Tool', 'Line Tool', 'Line Tool']","[[], ['AC'], ['BD', 'E'], ['AB']]",[]
+Iota,https://euclidea.fandom.com/wiki/Drop_a_Perpendicular*,"Description: Drop a perpendicular from the point to the line passing through the center of the circle using only a straightedge.Let O be the center of the circle, A be the given point, and B and C be the intersections of the circle and line.
+Tool List: ['Point Tool', 'Line Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB, intersecting the circle at D.
+<Line Tool>Construct line CD.
+<Line Tool>Construct line AC, intersecting the circle at E.
+<Line Tool>Construct line BE, intersecting CD at F.
+<Line Tool>Construct line AF.","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['O', 'A', 'B', 'C'], ['AB', 'D'], ['CD'], ['E', 'AC'], ['BE', 'F'], ['AF']]","['O', 'A', 'B', 'C']"
+Iota,https://euclidea.fandom.com/wiki/Midpoint*,"Description: Construct the midpoint of the segment using only a straightedge. To help you, a line parallel to the segment is given.Given the line AB.
+Tool List: ['Point Tool', 'Line Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a line connecting A with an arbitrary point C on the line.
+<Line Tool>Construct a line connecting B with another arbitrary point D on the line that intersects AC at E.
+<Line Tool>Construct line AD.
+<Line Tool>Construct line BC, intersecting AD at F.
+<Line Tool>Construct line EF, intersecting AB at G.
+<Point Tool>Point at G.","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Point Tool']","[['AB'], ['C', 'A'], ['D', 'E', 'AC', 'B'], ['AD'], ['F', 'BC'], ['EF', 'G'], []]",['AB']
+Iota,https://euclidea.fandom.com/wiki/Trisection_by_Trapezoid_Diagonals,"Description: 3L 5E 2V
+Tool List: ['Line Tool']
+Solution: ","<Line Tool>Construct line AF, intersecting BD at G.
+<Line Tool>Construct the line perpendicular to the bisector through G.","['Line Tool', 'Line Tool']","[[], ['AF', 'G', 'BD'], []]",[]
+Iota,https://euclidea.fandom.com/wiki/Minimum_Perimeter_-_2,"Description: Inscribe a triangle into the given one whose perimeter is the minimum possible.Let A, B, and C be the vertices of the triangle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the line perpendicular to AB through C, intersecting AB at D.
+<Perpendicular Tool>Construct the line perpendicular to AC through B, intersecting AC at E.
+<Perpendicular Tool>Construct the line perpendicular to BC through A, intersecting BC at F.
+<Line Tool>Construct line DE.
+<Line Tool>Construct line DF.
+<Line Tool>Construct line EF.","['Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Line Tool', 'Line Tool', 'Line Tool']","[['A', 'B', 'C'], ['AB', 'D'], ['E', 'AC'], ['F', 'BC'], ['DE'], ['DF'], ['EF']]","['A', 'B', 'C']"
+Iota,https://euclidea.fandom.com/wiki/Harmonic_Mean_of_Segments,"Description: Construct a point on the given ray to get a segment with length equal to the harmonic mean of the two adjacent segments.Given line AB, let C be the intersection of AB and the other line.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle C with radius AC, intersecting line C at D and AB at E.
+<Circle Tool>Construct circle D with radius DE.
+<Line Tool>Construct line DE, intersecting circle D at F.
+<Line Tool>Construct line BF, intersecting CD at G.
+<Point Tool>Point at G.","['Circle Tool', 'Circle Tool', 'Line Tool', 'Line Tool', 'Point Tool']","[['AB', 'C', 'AB'], ['AC', 'E', 'D'], ['DE'], ['F'], ['G', 'BF', 'CD'], []]","['AB', 'C', 'AB']"
+Iota,https://euclidea.fandom.com/wiki/Triangle_by_Angle_and_Centroid,"Description: Construct a segment connecting the sides of the angle to get a triangle whose centroid is in the point O.Let O be the vertex of the angle and A the given point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct the line parallel to one line through A, intersecting the other line at B.
+<Line Tool>Construct the line parallel to BO through A, intersecting the other line at C.
+<Circle Tool>Construct circle A with radius AB, intersecting AB at D.
+<Circle Tool>Construct circle A with radius AC, intersecting AC at E.
+<Line Tool>Construct line DE.","['Line Tool', 'Line Tool', 'Circle Tool', 'Circle Tool', 'Line Tool']","[['O', 'O', 'A'], ['B'], ['BO', 'C'], ['AB', 'D'], ['E', 'AC'], ['DE']]","['O', 'O', 'A']"
+Iota,https://euclidea.fandom.com/wiki/Triangle_Mid-Segment,"Description: Construct a mid-segment of the given acute triangle.Let A, B, and C be the vertices of the triangle.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at D.
+<Line Tool>Construct the line parallel to AC through D.","['Perpendicular Tool', 'Line Tool']","[['A', 'B', 'C'], ['AB', 'D'], ['AC']]","['A', 'B', 'C']"
+Kappa,https://euclidea.fandom.com/wiki/Tangent_of_Circle,"Description: Construct a tangent to the circle from the external point.Let A be the center and B the given point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB.
+<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at C.
+<Circle Tool>Construct circle C with radius AC, intersecting circle A at D.
+<Line Tool>Construct line BD.","['Line Tool', 'Perpendicular Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['AB'], ['C'], ['D', 'AC'], ['BD']]","['A', 'B']"
+Kappa,https://euclidea.fandom.com/wiki/Outer_Tangent,"Description: Construct an outer tangent between two circles.Let A and B be the centers of the circles.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB, intersecting the two circles at C and D, with C and D between A and B.
+<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at E.
+<Perpendicular Tool>Construct the perpendicular bisector of CD, intersecting AB at F.
+<Circle Tool>Construct circle E with radius AE, intersecting bisector F at G.
+<Circle Tool>Construct circle G with radius CG, intersecting circle A at H and circle B at I.
+<Line Tool>Construct line HI.","['Line Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['C', 'AB', 'D'], ['E'], ['F', 'CD'], ['G', 'AE'], ['H', 'CG', 'I'], ['HI']]","['A', 'B']"
+Kappa,https://euclidea.fandom.com/wiki/Inner_Tangent,"Description: Construct an inner tangent between two circles.Let A and B be the centers of the circles.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB, intersecting circle A at C and circle B at D, with C on the other side of A from B and D between A and B.
+<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at E.
+<Perpendicular Tool>Construct the perpendicular bisector of CD, intersecting AB at F.
+<Circle Tool>Construct circle E with radius AE, intersecting bisector F at G.
+<Circle Tool>Construct circle G with radius CG, intersecting circle A at H and circle B at I.
+<Line Tool>Construct line HI.","['Line Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['C', 'AB', 'D'], ['E'], ['F', 'CD'], ['G', 'AE'], ['H', 'CG', 'I'], ['HI']]","['A', 'B']"
+Kappa,https://euclidea.fandom.com/wiki/Rotation_90%C2%B0,"Description: Rotate the line segment 90° counterclockwise about the given point.Given the segment AB and O the point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AO.
+<Circle Tool>Construct circle O with radius AO.
+<Perpendicular Tool>Construct the line perpendicular to AO through O, intersecting circle O at C.
+<Circle Tool>Construct circle O with radius BO.
+<Perpendicular Tool>Construct the line perpendicular to AB through C, intersecting the latest circle at D.
+<Point Tool>Point at D.","['Line Tool', 'Circle Tool', 'Perpendicular Tool', 'Circle Tool', 'Perpendicular Tool', 'Point Tool']","[['AB', 'O'], ['AO'], [], ['C'], ['BO'], ['D'], []]","['AB', 'O']"
+Kappa,https://euclidea.fandom.com/wiki/Rotation_60%C2%B0,"Description: Rotate the line segment 60° clockwise about the given point.Given the segment AB and O the point.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle A with radius AO.
+<Circle Tool>Construct circle B with radius BO, intersecting circle A at C.
+<Circle Tool>Construct circle O with radius AO, intersecting circle A at D, with D being clockwise around O from A.
+<Line Tool>Construct line CD, intersecting circle B at E.
+<Point Tool>Point at E.","['Circle Tool', 'Circle Tool', 'Circle Tool', 'Line Tool', 'Point Tool']","[['AB', 'O'], ['AO', 'A'], ['BO', 'B', 'C'], ['D'], ['E', 'CD'], []]","['AB', 'O']"
+Kappa,https://euclidea.fandom.com/wiki/Segment_Trisection,"Description: Construct two points that divide the segment into 3 equal parts.Given the segment AB.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct circle A with radius AB.
+<Perpendicular Tool>Construct the perpendicular bisector of AB, intersecting AB at C and circle A at D.
+<Perpendicular Tool>Construct the perpendicular bisector of AD, intersecting CD at E.
+<Perpendicular Tool>Construct the line perpendicular to BE through E, intersecting AB at F.
+<Circle Tool>Construct circle C with radius CF, intersecting AB at G.
+<Point Tool>Point at G.","['Circle Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Perpendicular Tool', 'Circle Tool', 'Point Tool']","[['AB'], ['A'], ['C', 'D'], ['AD', 'E', 'CD'], ['BE', 'F'], ['CF', 'G'], []]",['AB']
+Kappa,https://euclidea.fandom.com/wiki/Segment_Trisection*,"Description: Construct points that divide the segment into three equal parts using only a straightedge. To help you, a line parallel to the segment is given.Given the segment AB.
+Tool List: ['Point Tool', 'Line Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct a line connecting A with an arbitrary point C on the line.
+<Line Tool>Construct a line connecting B with another arbitrary point D on the line that intersects AC at E.
+<Line Tool>Construct line AD.
+<Line Tool>Construct line BC, intersecting AD at F.
+<Line Tool>Construct line EF, intersecting CD at G.
+<Line Tool>Construct line AG, intersecting BD at H.
+<Line Tool>Construct line FH, intersecting AB at I and CD at J.
+<Line Tool>Construct line EJ, intersecting AB at K.
+<Point Tool>Point at I.
+<Point Tool>Point at K.","['Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Line Tool', 'Point Tool', 'Point Tool']","[['AB'], ['C', 'A'], ['D', 'E', 'AC', 'B'], ['AD'], ['F', 'BC'], ['EF', 'G', 'CD'], ['H', 'BD', 'AG'], ['FH', 'I', 'J'], ['EJ', 'K'], [], []]",['AB']
+Kappa,https://euclidea.fandom.com/wiki/Chord_Trisection,"Description: Construct a chord of the larger circle through the given point that is divided into three equal segments by the smaller concentric circle.Given the center A and point on the larger circle B.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AB, intersecting the smaller circle at C and D and the larger circle at E.
+<Circle Tool>Construct circle E with radius CD, intersecting the smaller circle at F.
+<Line Tool>Construct line BF.","['Line Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['C', 'AB', 'D', 'E'], ['F', 'CD'], ['BF']]","['A', 'B']"
+Kappa,https://euclidea.fandom.com/wiki/Three_Circles_-_1,"Description: Construct three circles with the given centers that are externally tangent each other.Given the points A, B, and C.
+Tool List: ['Line Tool']
+Solution: ",<Line Tool>Construct line AB.,['Line Tool'],"[['A', 'B', 'C'], ['AB']]","['A', 'B', 'C']"
+Kappa,https://euclidea.fandom.com/wiki/Secant_Bisection,"Description: Construct a secant through the given point that is divided into two equal segments by the circle.Given the point A and centre B.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct the line AB intersecting the circle at C and D.
+<Circle Tool>Construct the circle with centre B and radius AB, intersecting line AB at E.
+<Circle Tool>Construct the circle with centre E and radius CD, intersecting circle B at F.
+<Line Tool>Construct the line AF.","['Line Tool', 'Circle Tool', 'Circle Tool', 'Line Tool']","[['A', 'B'], ['C', 'AB', 'D'], ['E'], ['F', 'CD'], ['AF']]","['A', 'B']"
+Kappa,https://euclidea.fandom.com/wiki/Three_Circles_-_2,"Description: Construct three circles tangent to each other at the given points.Given the points A, B, and C.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AB.
+<Perpendicular Tool>Construct the perpendicular bisector of AC, intersecting the previous bisector at D.
+<Line Tool>Construct the line AD.
+<Perpendicular Tool>Construct the perpendicular to AD through A, intersecting the bisector of AB at E and the bisector of AC at F.
+<Circle Tool>Construct the circle with centre E and radius AE.
+<Circle Tool>Construct the circle with centre F and radius AF.
+<Line Tool>Construct the line BE.
+<Line Tool>Construct the line CF, intersecting BE at G.
+<Circle Tool>Construct the circle with centre G and radius BG.","['Perpendicular Tool', 'Perpendicular Tool', 'Line Tool', 'Perpendicular Tool', 'Circle Tool', 'Circle Tool', 'Line Tool', 'Line Tool', 'Circle Tool']","[['A', 'B', 'C'], ['AB'], ['AC', 'D'], ['AD'], ['F', 'E'], ['AE'], ['AF'], ['BE'], ['CF', 'G'], ['BG']]","['A', 'B', 'C']"
+Kappa,https://euclidea.fandom.com/wiki/Center_of_Rotation,"Description: Construct the center of rotation that transforms one of the given equal segments to the other one.Given one line AB and the other CD.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Perpendicular Tool>Construct the perpendicular bisector of AC.
+<Perpendicular Tool>Construct the perpendicular bisector of BD, intersecting the other bisector at E.
+<Point Tool>Point at E","['Perpendicular Tool', 'Perpendicular Tool', 'Point Tool']","[['AB', 'CD'], ['AC'], ['BD', 'E'], []]","['AB', 'CD']"
+Lambda,https://euclidea.fandom.com/wiki/Fourth_Proportional,"Description: Construct a point D on the ray OC such that the segment OD is the fourth proportional to the given segments.Given points O, A, B, and C.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Line Tool>Construct line AC.
+<Line Tool>Construct a line parallel to AC passing through B, intersecting ray OC at point D.
+<Point Tool>Mark point D.","['Line Tool', 'Line Tool', 'Point Tool']","[['D', 'OC', 'OD', 'O', 'A', 'B', 'C'], ['AC'], [], []]","['D', 'OC', 'OD', 'O', 'A', 'B', 'C']"
+Lambda,https://euclidea.fandom.com/wiki/Geometric_Mean_of_Segments,"Description: Construct a point on the given ray to get a segment with length equal to the geometric mean of two adjacent segments.Given line segment AB and ray O, where ray O extends from point O and |AO| = a and |BO| = b.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center O and radius |OA|, intersecting segment AB at C.
+<Circle Tool>Construct a circle with center C and radius |CO|, intersecting circle O at D and E.
+<Line Tool>Construct line DE.
+<Circle Tool>Construct a circle with center B and radius |BO|, intersecting circle B at F.
+<Circle Tool>Construct a circle with center O and radius |OF|, intersecting ray O at G.
+<Point Tool>Mark the point G.","['Circle Tool', 'Circle Tool', 'Line Tool', 'Circle Tool', 'Circle Tool', 'Point Tool']","[['AB', 'O', 'O', 'O', 'AO', 'BO'], ['C', 'OA'], ['CO', 'E', 'D'], ['DE'], ['F', 'B'], ['OF', 'G'], []]","['AB', 'O', 'O', 'O', 'AO', 'BO']"
+Lambda,https://euclidea.fandom.com/wiki/Golden_Section,"Description: Construct a point that divides the segment in the ""golden section"".Given line segment with points A and B.
+Tool List: ['Point Tool', 'Line Tool', 'Circle Tool', 'Perpendicular Bisector Tool', 'Perpendicular Tool', 'Angle Bisector Tool', 'Parallel Tool', 'Compass Tool', 'Intersect Tool']
+Solution: ","<Circle Tool>Construct a circle with center A and radius AB.
+<Perpendicular Tool>Construct the perpendicular bisector of AB, marking intersection with AB as point C, and marking intersection with circle A as point D.
+<Circle Tool>Construct a circle with center C and radius AB, marking intersection with circle A at E. E should be on the opposite side of AB from D, or else the solution will not work.
+<Line Tool>Construct line DE, intersecting with AB at point F.
+<Point Tool>Mark the point F.","['Circle Tool', 'Perpendicular Tool', 'Circle Tool', 'Line Tool', 'Point Tool']","[['A', 'B'], ['AB'], ['C', 'D'], ['E'], ['F', 'DE'], []]","['A', 'B']"