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Concurrent Tangent

Source: All-Russian MO 1999

January 10, 2011
geometryincentergeometric transformationreflectiongeometry proposed

Problem Statement

The incircle of △ABC\triangle ABC touch ABAB,BCBC,CACA at KK,LL,MM. The common external tangents to the incircles of △AMK\triangle AMK,△BKL\triangle BKL,△CLM\triangle CLM, distinct from the sides of △ABC\triangle ABC, are drawn. Show that these three lines are concurrent.
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