MathDB
Incircle, circumcenters and similar triangles

Source: Lusophon 2020 Day 2 #4

November 2, 2020
geometrycircumcirclesimilar triangles

Problem Statement

Let ABCABC be an acute triangle. Its incircle touches the sides BCBC, CACA and ABAB at the points DD, EE and FF, respectively. Let PP, QQ and RR be the circumcenters of triangles AEFAEF, BDFBDF and CDECDE, respectively. Prove that triangles ABCABC and PQRPQR are similar.
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