Let M be a point on the arc AB of the circumcircle of the triangle ABC which does not contain C. Suppose that the projections of M onto the lines AB and BC lie on the sides themselves, not on their extensions. Denote these projections by X and Y, respectively. Let K and N be the midpoints of AC and XY, respectively. Prove that ∠MNK=90∘ . geometrycircumcirclegeometric transformationdilationsimilar trianglesgeometry proposed