The circles of Miquel

Let ABCDEF be a complete quadrilateral (ABCD a quadrilateral and E and F the intersections of its opposite sides).
The circumcircles of $ \Delta $ADF, $ \Delta $ABE, $ \Delta $BCF, and $ \Delta $DCE intersect in M, the Miguel point.
If ABCD is a cycle quadrilateral then E, F and M are collinear.

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