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Geometry Mathley 4.2 perpendicular

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June 7, 2020
perpendicularcirclegeometry

Problem Statement

Let ABCABC be a triangle. (K)(K) is an arbitrary circle tangent to the lines AC,ABAC,AB at E,FE, F respectively. (K)(K) cuts BCBC at M,NM,N such that NN lies between BB and MM. FMFM intersects ENEN at II. The circumcircles of triangles IFNIFN and IEMIEM meet each other at JJ distinct from II. Prove that IJIJ passes through AA and KJKJ is perpendicular to IJIJ.
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