Question 27
Let $O$ be the circumcentre of the triangle $ABC$. Let $K$ and $L$ be the intersection points of the circumcircles of the triangles $BOC$ and $AOC$ with the bisectors of the angles at $A$ and $B$ respectively. Let $P$ be the midpoint of $\overline{KL}$, let $M$ be the point symmetric to $O$ with respect to $P$ and $N$ the point symmetric to $O$ with respect to $KL$. Prove that $KLMN$ is cyclic.