Question 18
Let $O$ be the center of the incircle of triangle $ABC$. The points $K$ and $L$ are the intersection points of the circumcircles of triangles $BOC$ and $AOC$, respectively with the bisectors of the angles at $A$ and $B$, $P$ is the middle point of $\overline{KL}$, $M$ is symmetrical to $O$ with respect to $P$ and $N$ is symmetrical to $O$ with respect to the line $KL$. Prove that the quadrilateral $KLMN$ is inscribed.
