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congruent squares inscribed in a triangle

Source: 1997 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p3

January 27, 2020
geometrySquarescongruent

Problem Statement

A square SaS_a is inscribed in an acute-angled triangle ABCABC with two vertices on side BCBC and one on each of sides ACAC and ABAB. Squares SbS_b and ScS_c are analogously inscribed in the triangle. For which triangles are the squares Sa,SbS_a,S_b, and ScS_c congruent?
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