Question 92
Let $M$ be the midpoint of the segment $AB$ and $C$ be an interior point of the segment $AB$, $C \neq M$. The isosceles triangles $ACK$ ($AK = CK$) and $BCL$ ($BL = CL$) lie in the same halfplane with respect to $AB$ and are such that the points $K, C, L$ and $M$ are concyclic. Prove that either $KL \parallel AB$ or $KA \perp LB$.