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Yum yum symmedia(m)n!

Source: Sharygin CR P10(Grades 8-9)

March 4, 2022
Sharygin Geometry OlympiadSharygin 2022geometry

Problem Statement

Let ω1\omega_1 be the circumcircle of triangle ABCABC and OO be its circumcenter. A circle ω2\omega_2 touches the sides AB,ACAB, AC, and touches the arc BCBC of ω1\omega_1 at point KK. Let II be the incenter of ABCABC. Prove that the line OIOI contains the symmedian of triangle AIKAIK.
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