Question 60
Let $CL$ and $CK$ be the inner and the outer bisectors of angle $ACB$ in $\triangle ABC$, $AC \gt BC$ and let $CM$ be its median. A point $P$ on $CM$ is such that the points $C, A_{1}, B_{1}$ and $P$ are concyclic, where $A_{1} = AP \rightarrow \cap BC$ and $B_{1} = BP \rightarrow \cap AC$. Prove that the points $C, K, L$ and $P$ are also concyclic.