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Segment equality with a rhombus

Source: Mexico National Olympiad Mock Exam 2017 P1

November 2, 2019
geometryCircumcenterrhombuscircumcircle

Problem Statement

Let ABCABC be a triangle with circumcenter OO. Point D,E,FD, E, F are chosen on sides AB,BCAB, BC and ACAC, respectively, such that ADEFADEF is a rhombus. The circumcircles of BDEBDE and CFECFE intersect AEAE at PP and QQ respectively. Show that OP=OQOP=OQ.
Proposed by Ariel García
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