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Prove B,E,F,Y cyclic

Source: Czech-Polish-Slovak Match 2019 P1

July 15, 2019
geometry

Problem Statement

Let ω\omega be a circle. Points A,B,C,X,D,YA,B,C,X,D,Y lie on ω\omega in this order such that BDBD is its diameter and DX=DY=DPDX=DY=DP , where PP is the intersection of ACAC and BDBD. Denote by E,FE,F the intersections of line XPXP with lines AB,BCAB,BC, respectively. Prove that points B,E,F,YB,E,F,Y lie on a single circle.
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