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excircle and incircle

Source: Moldova 2000 Grade 11 P3

April 26, 2021
geometryTriangle

Problem Statement

The excircle of a triangle ABCABC corresponding to AA touches the side BCBC at MM, and the point on the incircle diametrically opposite to its point of tangency with BCBC is denoted by NN. Prove that A,M,A,M, and NN are collinear.
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