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Geometry with bisectors

Source: Sharygin geometry olympiad 2015, grade 10, Final Round, Problem 1

July 17, 2018
geometry

Problem Statement

Let KK be an arbitrary point on side BCBC of triangle ABCABC, and KNKN be a bisector of triangle AKCAKC. Lines BNBN and AKAK meet at point FF, and lines CFCF and ABAB meet at point DD. Prove that KDKD is a bisector of triangle AKBAKB.
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