MathDB
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 aa 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 rr is the radius of the circle inscribed in the triangle, then r2<a<2rr\sqrt2 < a < 2r.