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Incircles and excircles

Source: Sharygin Geometry Olympiad 2012 - Problem 20

April 28, 2012
geometryincenterprojective geometrygeometric transformation

Problem Statement

Point DD lies on side ABAB of triangle ABCABC. Let ω1\omega_1 and Ω1,ω2\Omega_1,\omega_2 and Ω2\Omega_2 be the incircles and the excircles (touching segment ABAB) of triangles ACDACD and BCD.BCD. Prove that the common external tangents to ω1\omega_1 and ω2,\omega_2, Ω1\Omega_1 and Ω2\Omega_2 meet on ABAB.
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