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Triangle with 60° angle, projection of othocenter onto median

Source: Ukraine MO 2021 9.4

May 2, 2021
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle with ∠A=60∘\angle A = 60^\circ. Points PP and QQ are chosen on sides ABAB and ACAC, respectively, such that BP=PQ=QCBP = PQ = QC. Prove that the circumcircle of △APQ\triangle APQ passes through the projection of the orthocenter of ABCABC onto its AA-median.
Proposed by Fedir Yudin
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