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What are those points?

Source: India EGMO TST 2023/6

December 10, 2022
geometryIsosceles Triangleanglechasing

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB = AC. Suppose P,Q,RP,Q,R are points on segments AC,AB,BCAC, AB, BC respectively such that AP=QBAP = QB, ∠PBC=90∘−∠BAC\angle PBC = 90^\circ - \angle BAC and RP=RQRP = RQ. Let O1,O2O_1, O_2 be the circumcenters of △APQ\triangle APQ and △CRP\triangle CRP. Prove that BR=O1O2BR = O_1O_2.
Proposed by Atul Shatavart Nadig
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