square , 4 right isosceles triangles -VI Soros Olympiad 1999-00 Round 1 9.9
Source:
May 21, 2024
geometrysquare
Problem Statement
On the plane there are two isosceles non-intersecting right triangles and ( and are the hypotenuses, is a convex quadrilateral), and . Let's construct two more isosceles right triangles: (with hypotenuse located outside triangle ) and (with hypotenuse located outside triangle ). Prove that the line passes through a point such that is a square.