Question 24
In triangle $ABC$, such that $\angle ACB = 45^{\circ}$, let $O$ and $H$ be the circumcenter and orthocenter, respectively. The line passing through $O$ and perpendicular to $CO$ intersects $AC$ and $BC$ at $K$ and $L$, respectively. Prove that the perimeter of $KLH$ is equal to the diameter of the circumcircle of triangle $ABC$.