Problems(1)
The triangle ABC is inscribed in the circle ω. Points K,L,M are marked on the sides AB,BC,CA, respectively, and CM⋅CL=AM⋅BL. Ray LK intersects line AC at point P. The common chord of the circle ω and the circumscribed circle of the triangle KMP meets the segment AM at the point S. Prove that SK∥BC. circumcirclecircles