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AP passes through circumcenter of ABC, 2 reflections of a point wrt sides

Source: Mathematics Regional Olympiad of Mexico Center Zone 2019 P4

November 14, 2021
geometrycollinear

Problem Statement

Let ABCABC be a triangle with ∠BAC>90∘\angle BAC> 90 ^ \circ and DD a point on BCBC. Let EE and FFbe the reflections of the point DD about ABAB and ACAC, respectively. Suppose that BEBE and CFCF intersect at PP. Show that APAP passes through the circumcenter of triangle ABCABC.
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