# Problem 2

Let \(ABC\) be a triangle, and let \(M\) and \(N\) be the midpoints of \(AB\) and \(AC\), respectively. Choose points \(K\) and \(L\) strictly inside triangles \(BMC\) and \(BNC\), respectively, such that \(K\) lies strictly inside triangle \(ABL\) and \(L\) lies strictly inside triangle \(AKC\). Suppose that

\[
\angle KBA=\angle ACL,
\qquad
\angle LBK=\angle LNC,
\qquad
\angle LCK=\angle BMK.
\]

Let \(O\) be the circumcentre of triangle \(AKL\). Prove that

\[
OM=ON.
\]