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Incircle and median

Source: Sharygin Geometry Olympiad 2012 - Problem 8

April 28, 2012
geometryincentertrigonometrygeometric transformationhomothety

Problem Statement

Let BMBM be the median of right-angled triangle ABC(∠B=90∘)ABC (\angle B = 90^{\circ}). The incircle of triangle ABMABM touches sides AB,AMAB, AM in points A1,A2A_{1},A_{2}; points C1,C2C_{1}, C_{2} are defined similarly. Prove that lines A1A2A_{1}A_{2} and C1C2C_{1}C_{2} meet on the bisector of angle ABCABC.
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