CZ-SK-MO 1996 Problem 4

Points $A$ and $B$ on the rays $CX$ and $CY$ respectively of an acute angle $XCY$ are given so that $CX < CA = CB < CY$ . Construct a line meeting the ray $CX$ and the segments $AB,BC$ at $K,L,M$ , respectively, such that $KA \cdot YB = XA \cdot MB = LA\cdot LB \ne 0$ .