MathDB
Inner tangent passes through midpoint

Source: Sharygin Finals 2017, Problem 8.5

August 4, 2017
geometryTangentsmidpointsSquares

Problem Statement

A square ABCDABCD is given. Two circles are inscribed into angles AA and BB, and the sum of their diameters is equal to the sidelength of the square. Prove that one of their common tangents passes through the midpoint of ABAB.