Problem

Source: Serbia JBMO TST 2024 P4

Tags: geometry



Let $I$ be the incenter of a triangle $ABC$ with $AB \neq AC$. Let $M$ be the midpoint of $BC$, $M' \in BC$ be such that $IM'=IM$ and $K$ be the midpoint of the arc $BAC$. If $AK \cap BC=L$, show that $KLIM'$ is cyclic.