Let ABC be an acute triangle such that CA=CB with circumcircle ω and circumcentre O. Let tA and tB be the tangents to ω at A and B respectively, which meet at X. Let Y be the foot of the perpendicular from O onto the line segment CX. The line through C parallel to line AB meets tA at Z. Prove that the line YZ passes through the midpoint of the line segment AC.Proposed by Dominic Yeo, United Kingdom geometrycircumcircleBalkan Mathematics Olympiadprojective geometry