IOM 2019 Problem 3

In a non-equilateral triangle $ABC$ point $I$ is the incenter and point $O$ is the circumcenter. A line $s$ through $I$ is perpendicular to $IO$ . Line $\ell$ symmetric to like $BC$ with respect to $s$ meets the segments $AB$ and $AC$ at points $K$ and $L$ , respectively ( $K$ and $L$ are different from $A$ ). Prove that the circumcenter of triangle $AKL$ lies on the line $IO$ .

Dušan Djukić