The dynamic geometry figure below shows four green circles c1, c2, c3, and c4 passing through a point P. Circles c1 and c2 intersect at P12, and so on, P13, P23, P24, P14, and P34. Red Circle c123 passes through P12, P23, and P13, and so on. Prove that the four red circles pass through a point M.
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