MathDB
SK // BC wanted, CM x CL = AM x BL, circumcircle related

Source: SRMC 2020 P2 - Silk Road

August 18, 2020
circumcirclecircles

Problem Statement

The triangle ABC ABC is inscribed in the circle ω \omega . Points K,L,M K, L, M are marked on the sides AB,BC,CA AB, BC, CA , respectively, and CM⋅CL=AM⋅BL CM \cdot CL = AM \cdot BL . Ray LK LK intersects line AC AC at point P P . The common chord of the circle ω \omega and the circumscribed circle of the triangle KMP KMP meets the segment AM AM at the point S S . Prove that SK∥BC SK \parallel BC .
Back to ProblemsView on AoPS