Given lines 1 and 2, circle 3 passes through the points A, E, F, B, circle 4 passes through the points B, F, G, C, and circle 5 passes through the points C, G, H, D. Line AH and circle 3 meet at M, Line DE and circle 5 meet at N. Lines MB and HC meet at a point P and lines NC and EB meet at a point Q. Prove that BCQP is a cyclic quadrilateral. Post your solutions or ideas in the blog.