MMO 183 Moscow MO 1950 < 1/2 square’s perimeter lies outside the triangle.
Source:
August 6, 2019
geometryperimetersquarecircle
Problem Statement
A circle is inscribed in a triangle and a square is circumscribed around this circle so that no side of the square is parallel to any side of the triangle. Prove that less than half of the square’s perimeter lies outside the triangle.