For triangle ABC, P and Q satisfy ∠BPA+∠AQC=90∘. It is provided that the vertices of the triangle BAP and ACQ are ordered counterclockwise(or clockwise). Let the intersection of the circumcircles of the two triangles be N (A=N, however if A is the only intersection A=N), and the midpoint of segment BC be M. Show that the length of MN does not depend on P and Q. geometrycircumcirclegeometry unsolved