Unizor - Geometry2D - Similarity - Construction 1
Channel: Zor Shekhtman on UNIZOR Education
Date: 2012-08-09

1. Given an angle ∠AQB and a point P inside or outside of it (consider both cases). Draw a line XY through this point (points X and Y are, correspondingly, intersections of this line with legs QA and QB of a given angle) such that its segments from this point to legs of an angle PX and PY have a given ratio m:n.
2. Find a point inside a given triangle such that its distances from three sides of this triangle have a given ratio m:n:p.
3. Construct a triangle by its angle, one of its two sides that form this angle and the ratio of this side to the third side. How many solutions does this problem have?
4. Construct a triangle by its angle, an altitude originated at the vertex of this angle and the ratio of the segments of an opposite side this altitude divides it into.
5. Construct a triangle by its two angles and a sum of a side common for these angles with an altitude to this side from an opposite vertex.
6. Construct an isosceles triangle by its angle between equal sides and a difference between a base (a side opposite to this angle) and an altitude to it. Analyze a solution for any angle, depending on relative lengths of base and altitude.