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Geometry Mathley 14.1 equal circles

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June 7, 2020
equal circlescirclesgeometry

Problem Statement

A circle (K)(K) is through the vertices B,CB, C of the triangle ABCABC and intersects its sides CA,ABCA, AB respectively at E,FE, F distinct from C,BC, B. Line segment BEBE meets CFCF at GG. Let M,NM, N be the symmetric points of AA about F,EF, E respectively. Let P,QP, Q be the reflections of C,BC, B about AGAG. Prove that the circumcircles of triangles BPM,CQNBPM , CQN have radii of the same length.
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