Question 149
Triangle $ABC$ is inscribed into circle $\omega$. On sides $AB$, $BC$, $CA$ there are points $K$, $L$, $M$, respectively, such that $CM \cdot CL = AM \cdot BL$. Ray $LK$ intersects line $AC$ at point $P$. The common chord of $\omega$ and the circumscribed circle of $KMP$ intersects segment $AM$ at point $S$. Prove that $SK \parallel BC$. (Medeubek Kungozhin)