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.
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