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2017 China Second Round Test 2 Olympiad Problem 1

Source: 2017 China Second Round Test 2 Olympiad Problem 1

September 10, 2017
geometryincenter

Problem Statement

Given an isocleos triangle ABCABC with equal sides AB=ACAB=AC and incenter II.Let Γ1\Gamma_1be the circle centered at AA with radius ABAB,Γ2\Gamma_2 be the circle centered at II with radius BIBI.A circle Γ3\Gamma_3 passing through B,IB,I intersects Γ1\Gamma_1,Γ2\Gamma_2 again at P,QP,Q (different from BB) respectively.Let RR be the intersection of PIPI and BQBQ.Show that BR⊥CRBR \perp CR.
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