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SAMO 2022 Problem 4 - Two lines are equal

Source: South African Mathematics Olympiad 2022, Problem 4

August 11, 2022
geometrycircumcircleangle bisector

Problem Statement

Let ABCABC be a triangle with AB<ACAB < AC. A point PP on the circumcircle of ABCABC (on the same side of BCBC as AA) is chosen in such a way that BP=CPBP = CP. Let BPBP and the angle bisector of ∠BAC\angle BAC intersect at QQ, and let the line through QQ and parallel to BCBC intersect ACAC at RR. Prove that BR=CRBR = CR.
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