sum of diameters of incircles of triangles > sidelength of square
Source: 2014 Swedish Mathematical Competition p4
May 1, 2021
geometrycombinatorial geometrysquareGeometric Inequalities
Problem Statement
A square is cut into a finitely number of triangles in an arbitrary way. Show the sum of the diameters of the inscribed circles in these triangles is greater than the side length of the square.