Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: A square $P Q R S$ with sides of length 10 is rolled without slipping along a line. Initially $P$ and $Q$ are on the line and the first roll is around point $Q$ as shown in the diagram. The rolling stops when $P$ first returns to the line. What is the length of the curve that $P$ has travelled?
<image1>
Choices:
A. $10 \pi$
B. $5 \pi+5 \pi \sqrt{2}$
C. $10 \pi+5 \pi \sqrt{2}$
D. $5 \pi+10 \pi \sqrt{2}$
E. $10 \pi+10 \pi \sqrt{2}$
Answer: C
Problem: <image>Question: The diagram shows two ordinary dice. What is the total number of spots on all the faces that cannot be seen in the diagram? <image1>
Answer: 27
Problem: <image>Question: To complete the table, each cell must contain either 0 or 1 , and the total of each row and column must be 2 . What are the values of the entries $X$ and $Y$ ? <image1>
Choices:
A. $X=0, Y=0$
B. $X=0, Y=1$
C. $X=1, Y=0$
D. $X=1, Y=1$
E. It is impossible to complete.
Answer: A
Problem: <image>Question: In the calculation alongside, different letters represent different digits.
<image1>
Find the least possible answer to the subtraction shown.
Answer: 110
Problem: <image>Question: The diagram shows a triangle $J K L$ where two lines are drawn from each of the vertices $J$ and $K$ to points on the opposite sides. This divides the triangle into nine nonoverlapping sections. If instead, eight lines are drawn to the opposite sides, four from $J$ and four from $K$, how many nonoverlapping sections would the triangle be divided into? <image1>
Answer: 25
Problem: <image>Question: A dog is tied to the outside corner of a house by a rope of length $10 \mathrm{~m}$. The house is a rectangle with sides of length $6 \mathrm{~m}$ and $4 \mathrm{~m}$. What is the length (in metres) of the curved boundary of the area in which the dog can roam? <image1>
Choices:
A. $20 \pi$
B. $22 \pi$
C. $40 \pi$
D. $88 \pi$
E. $100 \pi$
Answer: A
Problem: <image>Question: A coin with diameter $1 \mathrm{~cm}$ rolls around the outside of a regular hexagon with edges of length $1 \mathrm{~cm}$ until it returns to its original position. In centimetres, what is the length of the path traced out by the centre of the coin? <image1>
Choices:
A. $6+\pi / 2$
B. $12+\pi$
C. $6+\pi$
D. $12+2 \pi$
E. $6+2 \pi$
Answer: C
Problem: <image>Question: An equilateral triangle and a regular hexagon are inscribed in a circle which is itself inscribed in an equilateral triangle. $L$ is the area of the large triangle, $S$ is the area of the smaller triangle and $H$ is the area of the hexagon. Which of these statements is true? <image1>
Choices:
A. $L=H+3 S$
B. $H=L S$
C. $H=\frac{1}{2}(L+S)$
D. $H=L-S$
E. $H=\sqrt{L S}$
Answer: E
Problem: <image>Question: Two circles have their centres on the same diagonal of a square. They touch each other and the sides of the square as shown. The square has side length $1 \mathrm{~cm}$. What is the sum of the radii of the circles in centimetres? <image1>
Choices:
A. $\frac{1}{2}$
B. $\frac{1}{\sqrt{2}}$
C. $\sqrt{2}-1$
D. $2-\sqrt{2}$
E. It depends on the relative sizes of the circles.
Answer: D
Problem: <image>Question: Five boxes contain cards as shown. Simon removes cards so that each box contains exactly one card, and the five cards remaining in the boxes can be used to spell his name. Which card remains in box 2 ?
<image1>
Choices:
A. S
B. I
C. M
D. O
E. N
Answer: D
Problem: <image>Question: Four unit squares are placed edge to edge as shown. What is the length of the line $P Q$ ? <image1>
Choices:
A. 5
B. $\sqrt{13}$
C. $\sqrt{5}+\sqrt{2}$
D. $\sqrt{5}$
E. 13
Answer: B
Problem: <image>Question: One face of a cardboard cube is cut along its diagonals, as shown.
Which of the following are not nets for this cube?
<image1>
<image2>
Choices:
A. 1 and 3
B. 1 and 5
C. 2 and 4
D. 2 and 4
E. 3 and 5
Answer: E
Problem: <image>Question: A parallelogram contains two identical regular hexagons. The hexagons share a common side, and each has two sides touching the sides of the parallelogram. What fraction of the parallelogram's area is shaded? <image1>
Choices:
A. $\frac{2}{3}$
B. $\frac{1}{2}$
C. $\frac{1}{3}$
D. $\frac{1}{4}$
E. $\frac{3}{5}$
Answer: B
Problem: <image>Question: On the number line below, each gap equals one unit. Six integers are marked as shown. At least two of the integers are divisible by 3 , and at least two of them are divisible by 5 . Which of the integers are divisible by 15 ?
<image1>
Choices:
A. $F$ and $K$
B. $G$ and $J$
C. $H$ and $I$
D. all six numbers
E. only one of them
Answer: A
Problem: <image>Question: In the diagram, triangle $J K L$ is isosceles with $J K=J L, P Q$ is perpendicular to $J K$, angle $K P L$ is $120^{\circ}$ and angle $J K P$ is $50^{\circ}$. What is the size of angle $P K L$ ? <image1>
Choices:
A. $5^{\circ}$
B. $10^{\circ}$
C. $15^{\circ}$
D. $20^{\circ}$
E. $25^{\circ}$
Answer: A
Problem: <image>Question: Three circles $C_{1}, C_{2}$ and $C_{3}$ of radii $1 \mathrm{~cm}, 2 \mathrm{~cm}$ and $3 \mathrm{~cm}$ respectively touch as shown. $C_{1}$ meets $C_{2}$ at $P$ and meets $C_{3}$ at $Q$. What is the length in centimetres of the longer arc of circle $C_{1}$ between $P$ and $Q$ ? <image1>
Choices:
A. $\frac{5 \pi}{4}$
B. $\frac{5 \pi}{3}$
C. $\frac{\pi}{2}$
D. $\frac{2 \pi}{3}$
E. $\frac{3 \pi}{2}$
Answer: E
Problem: <image>Question: The diagram shows the net of a regular octahedron. In a Magic Octahedron, the four numbers on the faces that meet at a vertex add up to make the same total for every vertex. If the letters $F, G, H, J$ and $K$ are replaced with the numbers $2,4,6,7$, and 8 , in some order, to make a Magic Octahedron, what is the value of $G+J$ ? <image1>
Answer: 6
Problem: <image>Question: An $n$-pyramid is defined to be a stack of $n$ layers of balls, with each layer forming a triangular array. The layers of a 3-pyramid are shown in the diagram.
An 8-pyramid is now formed where all the balls on the outside of the 8 -pyramid are black (including the base layer) and the balls on the inside are all white. How many layers are there in the white pyramid?
<image1>
Answer: 4
Problem: <image>Question: Sixteen unit squares are arranged to form a square array as shown in the diagram. What is the maximum number of diagonals that can be drawn in these unit squares so that no two diagonals share a common point (including endpoints)?
<image1>
Answer: 10
Problem: <image>Question: In the diagram, $K L M N$ is a unit square. Arcs of radius one unit are drawn using each of the four corners of the square as centres. The arcs centred at $K$ and $L$ intersect at $Q$; the arcs centred at $M$ and $N$ intersect at $P$. What is the length of $P Q$ ? <image1>
Choices:
A. $2-\sqrt{2}$
B. $\frac{3}{4}$
C. $\sqrt{5}-\sqrt{2}$
D. $\frac{\sqrt{3}}{3}$
E. $ \sqrt{3}-1$
Answer: E
Problem: <image>Question: The diagram shows a triangle and three circles whose centres are at the vertices of the triangle. The area of the triangle is $80 \mathrm{~cm}^{2}$ and each of the circles has radius $2 \mathrm{~cm}$. What is the area, in $\mathrm{cm}^{2}$, of the shaded area? <image1>
Choices:
A. 76
B. $80-2 \pi$
C. $40-4 \pi$
D. $80-\pi$
E. $78 \pi$
Answer: B
Problem: <image>Question: The three angle bisectors of triangle $L M N$ meet at a point $O$ as shown. Angle $L N M$ is $68^{\circ}$. What is the size of angle $L O M$ ? <image1>
Choices:
A. $120^{\circ}$
B. $124^{\circ}$
C. $128^{\circ}$
D. $132^{\circ}$
E. $136^{\circ}$
Answer: B
Problem: <image>Question: The diagram shows two identical large circles and two identical smaller circles whose centres are at the corners of a square. The two large circles are touching, and they each touch the two smaller circles. The radius of the small circles is $1 \mathrm{~cm}$. What is the radius of a large circle in centimetres? <image1>
Choices:
A. $1+\sqrt{2}$
B. $\sqrt{5}$
C. $\sqrt{2}$
D. $\frac{5}{2}$
E. $\frac{4}{5} \pi$
Answer: A
Problem: <image>Question: Three circular hoops are joined together so that they intersect at rightangles as shown. A ladybird lands on an intersection and crawls around the outside of the hoops by repeating this procedure: she travels along a quarter-circle, turns $90^{\circ}$ to the right, travels along a quarter-circle and turns $90^{\circ}$ to the left. Proceeding in this way, how many quarter-circles will she travel along before she first returns to her starting point? <image1>
Answer: 6
Problem: <image>Question: Barbara wants to place draughts on a $4 \times 4$ board in such a way that the number of draughts in each row and in each column are all different (she may place more than one draught in a square, and a square may be empty). What is the smallest number of draughts that she would need? <image1>
Answer: 14
Problem: <image>Question: Four cubes, each with surface area $24 \mathrm{~cm}^{2}$, are placed together to form a cuboid as shown. What is the surface area of this cuboid, in $\mathrm{cm}^{2}$ ? <image1>
Answer: 64
Problem: <image>Question: A rectangular strip of paper is folded in half three times, with each fold line parallel to the short edges. It is then unfolded so that the seven folds up or down can all be seen. Which of the following strips, viewed from a long edge, could not be made in this way? <image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Six points are marked on a sheet of squared paper as shown. Which of the following shapes cannot be made by connecting some of these points using straight lines? <image1>
Choices:
A. parallelogram
B. trapezium
C. right-angled triangle
D. obtuse-angled triangle
E. all the shapes $\mathrm{A}-\mathrm{D}$ can be made
Answer: E
Problem: <image>Question: The diagram shows a square $P Q R S$ and two equilateral triangles $R S U$ and PST. PQ has length 1 . What is the length of $T U$ ? <image1>
Choices:
A. $\sqrt{2}$
B. $\frac{\sqrt{3}}{2}$
C. $\sqrt{3}$
D. $\sqrt{5}-1$
E. $\sqrt{6}-1$
Answer: A
Problem: <image>Question: In the diagram, angle $P Q R$ is $20^{\circ}$, and the reflex angle at $P$ is $330^{\circ}$. The line segments $Q T$ and $S U$ are perpendicular. What is the size of angle RSP? <image1>
Choices:
A. $10^{\circ}$
B. $20^{\circ}$
C. $30^{\circ}$
D. $40^{\circ}$
E. $50^{\circ}$
Answer: D
Problem: <image>Question: A circle of radius $4 \mathrm{~cm}$ is divided into four congruent parts by arcs of radius $2 \mathrm{~cm}$ as shown. What is the length of the perimeter of one of the parts, in $\mathrm{cm}$ ? <image1>
Choices:
A. $2 \pi$
B. $4 \pi$
C. $6 \pi$
D. $8 \pi$
E. $12 \pi$
Answer: C
Problem: <image>Question: The scatter graph shows the distance run and time taken by five students during a training session. Who ran with the fastest average speed? <image1>
Choices:
A. Alicia
B. Bea
C. Carlos
D. Dani
E. Ernesto
Answer: D
Problem: <image>Question: A triangular piece of paper is folded along the dotted line shown in the left-hand diagram to form the heptagon shown in the right-hand diagram. The total area of the shaded parts of the heptagon is $1 \mathrm{~cm}^{2}$. The area of the original triangle is $1 \frac{1}{2}$ times the area of the heptagon. What is the area of the original triangle, in $\mathrm{cm}^{2}$ ? <image1>
Answer: 3
Problem: <image>Question: In a supermarket trolley park, there are two lines of tightly-packed trolleys. The first line has ten trolleys and is $2.9 \mathrm{~m}$ long. The second line has twenty trolleys and is $4.9 \mathrm{~m}$ long. What is the length of one trolley, in $\mathrm{m}$ ? <image1>
Answer: 1.1
Problem: <image>Question: The diagram shows a trapezium $F G H I$ with $F G$ parallel to $I H$. GH and FI both have length 2. The point $M$ is the midpoint of $F I$ and $\angle H M G=90^{\circ}$. What is the length of the perimeter of the trapezium? <image1>
Answer: 6
Problem: <image>Question: The diagram shows a square with sides of length 2. Four semicircles are drawn whose centres are the four vertices of the square. These semicircles meet at the centre of the square, and adjacent semicircles meet at their ends. Four circles are drawn whose centres lie on the edges of the square and which each touch two semicircles. What is the total shaded area? <image1>
Choices:
A. $4 \pi(3-2 \sqrt{2})$
B. $4 \pi \sqrt{2}$
C. $\frac{16}{9} \pi$
D. $\pi$
E. $\frac{4}{\sqrt{2}} \pi$
Answer: A
Problem: <image>Question: An oval is constructed from four arcs of circles. Arc $P Q$ is the same as arc $R S$, and has radius $1 \mathrm{~cm}$. Arc $Q R$ is the same as arc PS. At the points $P, Q, R, S$ where the arcs touch, they have a common tangent. The oval touches the midpoints of the sides of a rectangle with dimensions $8 \mathrm{~cm}$ by $4 \mathrm{~cm}$. What is the radius of the arc $P S$, in $\mathrm{cm}$ ? <image1>
Answer: 6
Problem: <image>Question: A bar code of the type shown is composed of alternate strips of black and white, always beginning and ending with a black strip. Each strip in the bar code has width either 1 or 2 , and the total width of the bar code is 12 . Two bar codes are different if they read differently from left to right. How many different bar codes of this type can be made? <image1>
Answer: 116
Problem: <image>Question: The figure shows a hexagonal lattice. Numbers are to be placed at each of the dots $\cdot$ in such a way that the sum of the two numbers at the ends of each segment is always the same. Two of the numbers are already given. What number is $x$ ? <image1>
Answer: 1
Problem: <image>Question: One of the line segments shown on the grid is the image produced by a rotation of the other line segment. Which of the points $T, U, V$, $W$ could be the centre of such a rotation? <image1>
Choices:
A. only $T$
B. only $U$
C. either of $U$ and $W$
D. any of $U, V$ and $W$
E. any of $T, U, V$ and $W$
Answer: C
Problem: <image>Question: The diagram shows a shape made from a regular hexagon of side one unit, six triangles and six squares. What is the perimeter of the shape? <image1>
Choices:
A. $6(1+\sqrt{2})$
B. $6\left(1+\frac{1}{2} \sqrt{3}\right)$
C. $12$
D. $6+3 \sqrt{2}$
E. $9$
Answer: C
Problem: <image>Question: A marble with radius $15 \mathrm{~cm}$ fits exactly under a cone as shown in the diagram. The slant height of the cone is equal to the diameter of its base. What is the height of the cone in $\mathrm{cm}$ ? <image1>
Answer: 45
Problem: <image>Question: Barbara wants to place draughts on a $4 \times 4$ board in such a way that the number of draughts in each row is equal to the number shown at the end of the row, and the number of draughts in each column is equal to the number shown at the bottom of the column. No more than one draught is to be placed in any cell. In how many ways can this be done? <image1>
Answer: 5
Problem: <image>Question: Nik wants to write integers in the cells of a $3 \times 3$ table so that the sum of the numbers in any $2 \times 2$ square is 10 . He has already written five numbers in the table as shown. What is the sum of the four missing numbers?
<image1>
Answer: 12
Problem: <image>Question: During a rough sailing trip, Jacques tried to sketch a map of his village. He managed to draw the four streets, the seven places where they cross and the houses of his friends. The houses are marked on the correct streets, and the intersections are correct, however, in reality, Arrow Street, Nail Street and Ruler Street are all absolutely straight. The fourth street is Curvy Street. Who lives on Curvy Street?
<image1>
Choices:
A. Adeline
B. Benjamin
C. Carole
D. David
E. It is impossible to tell without a better map
Answer: A
Problem: <image>Question: Simone has a cube with sides of length $10 \mathrm{~cm}$, and a pack of identical square stickers. She places one sticker in the centre of each face of the cube, and one across each edge so that the stickers meet at their corners, as shown in the diagram. What is the total area in $\mathrm{cm}^{2}$ of the stickers used by Simone? <image1>
Answer: 225
Problem: <image>Question: In triangle $P Q R$, a point $S$ is chosen on the line segment $Q R$, then a point $T$ is chosen on the line segment $P S$. Considering the nine marked angles, what is the smallest number of different values that these nine angles could take? <image1>
Answer: 3
Problem: <image>Question: A cuboid is made of four pieces as shown. Each piece consists of four cubes and is a single colour. What is the shape of the white piece? <image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: The triangle $H I J$ has the same area as the square $F G H I$, whose sides are of length $4 \mathrm{~cm}$. What is the perpendicular distance, in $\mathrm{cm}$, of the point $J$ from the line extended through $F$ and $G$ ? <image1>
Answer: 12
Problem: <image>Question: Six identical circles fit together tightly in a rectangle of width $6 \mathrm{~cm}$ as shown. What is the height, in $\mathrm{cm}$, of the rectangle? <image1>
Choices:
A. 5
B. $2 \sqrt{3}+2$
C. $3 \sqrt{2}$
D. $3 \sqrt{3}$
E. 6
Answer: B
Problem: <image>Question: The right-angled triangle shown has sides of length $5 \mathrm{~cm}, 12$ $\mathrm{cm}$ and $13 \mathrm{~cm}$. What, in $\mathrm{cm}$, is the radius of the inscribed semicircle whose diameter lies on the side of length $12 \mathrm{~cm}$ ? <image1>
Choices:
A. $8 / 3$
B. $10 / 3$
C. $11 / 3$
D. 4
E. $13 / 3$
Answer: B
Problem: <image>Question: Numbers are to be placed into the table shown, one number in each cell, in such a way that each row has the same total, and each column has the same total. Some of the numbers are already given. What number is $x$ ? <image1>
Answer: 4
Problem: <image>Question: A rectangular piece of paper $F G H I$ with sides of length $4 \mathrm{~cm}$ and $16 \mathrm{~cm}$ is folded along the line $M N$ so that the vertex $G$ coincides with the vertex $I$ as shown. The outline of the paper now makes a pentagon $F M N H^{\prime} I$. What is the area, in $\mathrm{cm}^{2}$, of the pentagon $F M N H^{\prime} I$ ? <image1>
Answer: 47
Problem: <image>Question: The diagram shows a square with sides of length $4 \mathrm{~mm}$, a square with sides of length $5 \mathrm{~mm}$, a triangle with area $8 \mathrm{~mm}^{2}$, and a parallelogram. What is the area, in $\mathrm{mm}^{2}$, of the parallelogram? <image1>
Answer: 16
Problem: <image>Question: Carlos creates a game. The diagram shows the board for the game. At the start, the kangaroo is at the school $(\mathrm{S})$. According to the rules of the game, from any position except home $(\mathrm{H})$, the kangaroo can jump to either of the two neighbouring positions. When the kangaroo lands on $\mathrm{H}$ the game is over. In how many ways can the kangaroo move from $\mathrm{S}$ to $\mathrm{H}$ in exactly 13 jumps? <image1>
Answer: 64
Problem: <image>Question: The diagram shows six identical squares, each containing a shaded region.
<image1> How many of the regions have perimeter equal in length to the perimeter of one of the squares?
Answer: 4
Problem: <image>Question: The outside of a $2 \times 2 \times 2$ cube is painted with black and white squares in such a way that it appears as if it was built using alternate black cubes and white cubes, as shown. Which of the following is a net of the painted cube?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: The trapezium shown in the diagram is rotated anti-clockwise by $90^{\circ}$ around the origin $O$, and then reflected in the $x$-axis. Which of the following shows the end result of these transformations? <image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: The diagram shows an equilateral triangle RST and also the triangle $T U V$ obtained by rotating triangle $R S T$ about the point $T$. Angle $R T V=70^{\circ}$. What is angle $R S V$ ? <image1>
Choices:
A. $20^{\circ}$
B. $25^{\circ}$
C. $30^{\circ}$
D. $35^{\circ}$
E. $40^{\circ}$
Answer: D
Problem: <image>Question: The diagram shows a shape made from six squares, each measuring $1 \mathrm{~cm}$ by $1 \mathrm{~cm}$. The shape has perimeter of length $14 \mathrm{~cm}$. The zigzag shape is then continued until it has 2013 squares. What is the length, in $\mathrm{cm}$, of the perimeter of the new shape? <image1>
Answer: 4028
Problem: <image>Question: The points $P$ and $Q$ are opposite vertices of a regular hexagon and the points $R$ and $S$ are midpoints of opposite edges, as shown. The area of the hexagon is $60 \mathrm{~cm}^{2}$. What is the product of the lengths, in cms, of $P Q$ and $R S$ ? <image1>
Answer: 80
Problem: <image>Question: The rectangle $A B C D$ lies below the $x$-axis, and to the left of the $y$-axis. The edges of the rectangle are parallel to the coordinate axes. For each point $A, B, C, D$, the $y$-coordinate is divided by the $x$-coordinate. Which of the points yields the smallest value from this calculation? <image1>
Choices:
A. A
B. C
C. C
D. D
E. it depends on the size of the rectangle
Answer: A
Problem: <image>Question: In quadrilateral $P Q R S, \angle P Q R=59^{\circ}, \angle R P Q=60^{\circ}$, $\angle P R S=61^{\circ}$ and $\angle R S P=60^{\circ}$, as shown. Which of the following line segments is the longest? <image1>
Choices:
A. $P Q$
B. $P R$
C. $P S$
D. $Q R$
E. $R S$
Answer: A
Problem: <image>Question: How many different paths are there between points $P$ and $Q$, only travelling along the edges in the direction of the arrows shown? <image1>
Answer: 12
Problem: <image>Question: Several non-overlapping isosceles triangles have vertex $O$ in common. Every triangle shares an edge with each immediate neighbour. The smallest of the angles at $O$ has size $m^{\circ}$, where $m$ is a positive integer and the other triangles have angles at $O$ of size $2 m^{\circ}, 3 m^{\circ}, 4 m^{\circ}$, and so on. The diagram shows an arrangement of five such triangles. What is the smallest value of $m$ for which such a set of triangles exists?
<image1>
Answer: 3
Problem: <image>Question: If $r, s$, and $t$ denote the lengths of the 'lines' in the picture, then which of the following inequalities is correct? <image1>
Choices:
A. $r<s<t$
B. $r<t<s$
C. $s<r<t$
D. $s<t<r$
E. $t<s<r$
Answer: E
Problem: <image>Question: The big wheel of this penny-farthing bicycle has perimeter 4.2 metres. The small wheel has perimeter 0.9 metres. At a certain moment, the valves of both wheels are at their lowest points. The bicycle begins to roll.
How many metres will the bicycle have rolled forward when both valves are next at their lowest points at the same time?
<image1>
Answer: 12.6
Problem: <image>Question: The diagram shows a regular octagon, with a line drawn between two of its vertices. The shaded area measures $3 \mathrm{~cm}^{2}$.
What is the area of the octagon in square centimetres? <image1>
Answer: 12
Problem: <image>Question: The diagram shows a special die. Each pair of numbers on opposite faces has the same sum. The numbers on the hidden faces are all prime numbers. Which number is opposite to the 14 shown?
<image1>
Answer: 23
Problem: <image>Question: The picture shows seven points and the connections between them. What is the least number of connecting lines that could be added to the picture so that each of the seven points has the same number of connections with other points? (Connecting lines are allowed to cross each other.)
<image1>
Answer: 9
Problem: <image>Question: The picture shows the same cube from two different views. It is built from 27 smaller cubes, some of which are grey and some white.
What is the largest number of grey cubes there could be?
<image1>
Answer: 9
Problem: <image>Question: In the picture, $P T$ is a tangent to the circle with centre $O$ and $P S$ is the angle bisector of angle $R P T$.
What is the size of angle TSP? <image1>
Choices:
A. $30^{\circ}$
B. $45^{\circ}$
C. $50^{\circ}$
D. $60^{\circ}$
E. It depends on the position of point $P$.
Answer: B
Problem: <image>Question: The diagram shows a triangle $F H G$ with $F H=6, G H=8$ and $F G=10$. The point $I$ is the midpoint of $F G$, and HIJK is a square. The line segment $I J$ intersects $G H$ at $L$. What is the area of the shaded quadrilateral HLJK? <image1>
Choices:
A. $\frac{124}{8}$
B. $\frac{125}{8}$
C. $\frac{126}{8}$
D. $\frac{127}{8}$
E. $\frac{128}{8}$
Answer: B