Given the line AB, let M be a point on it. Towards the same side of the plane and with bases AM and MB, squares AMCD and MBEF are constructed. Let N be the point (different from M) where the circumcircles circumscribed to both squares intersect and let N1 be the point where the lines BC and AF intersect. Prove that the points N and N1 coincide. Prove that as the point M moves on the line AB, the line MN moves always passing through a fixed point. geometryFixed pointchilean NMO