Let the points M and N be the intersections of the inscribed circle of the right-angled triangle ABC, with sides AB and CA respectively , and points P and Q respectively be the intersections of the ex-scribed circles opposite to vertices B and C with direction BC. Prove that the quadrilateral MNPQ is a cyclic if and only if the triangle ABC is right-angled with a right angle at the vertex A. geometrycyclic quadrilateralConcyclicincircleexcirclesright triangle