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2017 IGO Intermediate P2

Source: 4th Iranian Geometry Olympiad (Intermediate) P2

September 15, 2017
IGOIrangeometry

Problem Statement

Two circles ω1,ω2\omega_1,\omega_2 intersect at A,BA,B. An arbitrary line through BB meets ω1,ω2\omega_1,\omega_2 at C,DC,D respectively. The points E,FE,F are chosen on ω1,ω2\omega_1,\omega_2 respectively so that CE=CB, BD=DFCE=CB,\ BD=DF. Suppose that BFBF meets ω1\omega_1 at PP, and BEBE meets ω2\omega_2 at QQ. Prove that A,P,QA,P,Q are collinear.
Proposed by Iman Maghsoudi
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