Question 2
Let $ABC$ be a triangle and let points $M$ and $N$ be the midpoints of sides $AB$ and $AC$, respectively. Let points $K$ and $L$ be chosen strictly inside triangles $BMC$ and $BNC$, respectively, such that $K$ lies strictly inside triangle $ABL$ and $L$ lies strictly inside triangle $AKC$. Suppose that
$$\angle KBA=\angle ACL,\quad \angle LBK=\angle LNC,\quad \angle LCK=\angle BMK.$$
Let $O$ be the circumcentre of triangle $AKL$. Prove that $OM=ON$.
$$\angle KBA=\angle ACL,\quad \angle LBK=\angle LNC,\quad \angle LCK=\angle BMK.$$
Let $O$ be the circumcentre of triangle $AKL$. Prove that $OM=ON$.