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PQ passes through circumcenter, similar triangles of projections of 2 points,

Source: 2008 Oral Moscow Geometry Olympiad grades 10-11 p6

October 14, 2020
geometrysimilar trianglesCircumcentercollinear

Problem Statement

Given a triangle ABCABC and points PP and QQ. It is known that the triangles formed by the projections PP and QQ on the sides of ABCABC are similar (vertices lying on the same sides of the original triangle correspond to each other). Prove that line PQPQ passes through the center of the circumscribed circle of triangle ABCABC.
(A. Zaslavsky)
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