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Crowded Geometry with Two Circles

Source: Germany TST 2011 P1

April 11, 2020
geometry

Problem Statement

Two circles ω,Ω\omega , \Omega intersect in distinct points A,BA,B a line through BB intersects ω,Ω\omega , \Omega in C,DC,D respectively such that BB lies between C,DC,D another line through BB intersects ω,Ω\omega , \Omega in E,FE,F respectively such that EE lies between B,FB,F and FE=CDFE=CD. Furthermore CFCF intersects ω,Ω\omega , \Omega in P,QP,Q respectively and M,NM,N are midpoints of the arcs PB,QBPB,QB. Prove that CNMFCNMF is a cyclic quadrilateral.
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