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Geometry Mathley 8.2 line tangent wanted

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June 7, 2020
tangentcircumcircleincentergeometry

Problem Statement

Let ABCABC be a triangle, dd a line passing through AA and parallel to BCBC. A point MM distinct from AA is chosen on dd. II is the incenter of triangle ABC,K,LABC, K,L are the the points of symmetry of MM about IB,ICIB, IC. Let BKBK meet CLCL at NN. Prove that ANAN is tangent to circumcircle of triangle ABCABC.
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