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Brocard point on median

Source: 10.6 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 7, 2024
geogeometry

Problem Statement

A point PP lies on one of medians of triangle ABCABC in such a way that ∠PAB=∠PBC=∠PCA\angle PAB =\angle PBC =\angle PCA. Prove that there exists a point QQ on another median such that ∠QBA=∠QCB=∠QAC\angle QBA=\angle QCB =\angle QAC.
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