Unizor - Geometry2D - Similarity - Construction 2
Channel: Zor Shekhtman on UNIZOR Education
Date: 2012-08-11

1. Find a point C outside segment AB so that CA : CB = m : n. 
2. Inscribe a triangle into a given circle by its one side and a ratio m and n of two other sides.
3. Inscribe a triangle into a given circle by its one side and a median to one of the other sides.
4. Inscribe a square into a given segment such that one of its sides lies on a chord, while two opposite vertices of this square lie on an arc.
5. Inscribe a square into a given triangle such that one of its sides lies on one side of a triangle, while two opposite vertices of this square lie on two other sides of a triangle.
6. Construct a triangle similar to a given one around a given square such that one side of a given square lies on one side of a triangle, while two opposite vertices of this square lie on two other sides of a triangle.
7. Inscribe a rectangle into a given triangle such that one of its sides lies on one side of a triangle, while two opposite vertices of this rectangle lie on two other sides of a triangle and the ratio between two sides of this rectangle that form the right angle is given as m:n.
8. Construct a triangle similar to a given one around a given rectangle such that one side of a given rectangle lies on one side of a triangle, while two opposite vertices of this rectangle lie on two other sides of a triangle.