Let ABC be a triangle with CA=CB and ∠ACB=120∘, and let M be the midpoint of AB. Let P be a variable point of the circumcircle of ABC, and let Q be the point on the segment CP such that QP=2QC. It is given that the line through P and perpendicular to AB intersects the line MQ at a unique point N.
Prove that there exists a fixed circle such that N lies on this circle for all possible positions of P. geometryEGMOTrianglecircleEGMO 2018