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Geometry( SMO 2012)

Source: SMO 2012 Q1

June 30, 2012
geometrytrigonometrygeometry proposed

Problem Statement

The incircle with centre II of the triangle ABCABC touches the sides BC,CABC, CA and ABAB at D,E,FD, E, F respectively. The line IDID intersects the segment EFEF at KK. Proof that A,K,MA, K, M collinear, where MM is the midpoint of BCBC.
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