Problem

Source: IrMO 2022

Tags: geometry, circles, cyclic quadrilateral



7. The four Vertices of a quadrilateral ABCD lie on the circle with diameter AB. The diagonals of ABCD intersect at E, and the lines AD and BC intersect at F. Line FE meets AB at K and line DK meets the circle again at L. Prove that CL is perpendicular to AB.