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Bundeswettbewerb Mathematik 1980 Problem 2.3

Source: Bundeswettbewerb Mathematik 1980 Round 2

September 23, 2022
geometryTrianglesimilarcircumcirle

Problem Statement

In a triangle ABCABC, points P,QP, Q and R R distinct from the vertices of the triangle are chosen on sides AB,BCAB, BC and CACA, respectively. The circumcircles of the triangles APRAPR, BPQBPQ, and CQRCQR are drawn. Prove that the centers of these circles are the vertices of a triangle similar to triangle ABCABC.
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