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Circumcenter on IO

Source: International Olympiad of Metropolises 2019 P3

September 3, 2019
geometrycircumcircleincenter

Problem Statement

In a non-equilateral triangle ABCABC point II is the incenter and point OO is the circumcenter. A line ss through II is perpendicular to IOIO. Line \ell symmetric to like BCBC with respect to ss meets the segments ABAB and ACAC at points KK and LL, respectively (KK and LL are different from AA). Prove that the circumcenter of triangle AKLAKL lies on the line IOIO.
Dušan Djukić