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$DE$ bisects sides $AB$ and $AC$

Source: ARMO 1997, 10.7

April 20, 2013
geometryAsymptoteparallelogramgeometry proposed

Problem Statement

The incircle of triangle ABCABC touches sides ABAB;BCBC;CACA at MM;NN;KK, respectively. The line through AA parallel to NKNK meets MNMN at DD. The line through AA parallel to MNMN meets NKNK at EE. Show that the line DEDE bisects sides ABAB and ACAC of triangle ABCABC. M. Sonkin
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