IMO-2026, Problem 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 inside triangles BMC and BNC, respectively, such that K lies inside the angle LBA, L lies inside the angle ACK, and

∠ KBA= ∠ ACL, ∠ LBK= ∠ LNC, ∠ LCK= ∠ BMK

Let O be the circumcentre of triangle AKL. Prove that OM = ON.

(Proposed by Mykhailo Shtandenko, Ukraine)