MathDB

10

Part of 2022 Sharygin Geometry Olympiad

Problems(1)

Yum yum symmedia(m)n!

Source: Sharygin CR P10(Grades 8-9)

3/4/2022
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.
Sharygin Geometry OlympiadSharygin 2022geometry