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Show that CK is parallel to AB

Source: Sharygin First Round 2013, Problem 16

April 8, 2013
geometryincenterangle bisectorParallel Linesprojective geometry

Problem Statement

The incircle of triangle ABCABC touches BCBC, CACA, ABAB at points A1A_1, B1B_1, C1C_1, respectively. The perpendicular from the incenter II to the median from vertex CC meets the line A1B1A_1B_1 in point KK. Prove that CKCK is parallel to ABAB.
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