MMO 330 Moscow MO 1956 r\sqrt2 < a < 2r, square inscribed in triangle
Source:
August 19, 2019
geometric inequalitygeometryinradiussquareinscribed
Problem Statement
A square of side is inscribed in a triangle so that two of the square’s vertices lie on the base, and the other two lie on the sides of the triangle. Prove that if is the radius of the circle inscribed in the triangle, then .