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Nice geometry proposed by Pavel Kozhevnikov

Source:

October 1, 2019
geometryincentercircumcircle

Problem Statement

Let I,O I,O denote the incenter, respectively, the circumcenter of a triangle ABC. ABC. The A-excircle A\text{-excircle} touches the lines AB,AC,BC AB,AC,BC at K,L, K,L, respectively, M. M. The midpoint of KL KL lies on the circumcircle of ABC. ABC. Show that the points I,M,O I,M,O are collinear.
Павел Кожевников
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