## The circles of Miquel

Posted December 30th, 2007 by Isoscel

Let ABCDEF be a complete quadrilateral (ABCD a quadrilateral and E and F the intersections of its opposite sides).

The circumcircles of ADF, ABE, BCF, and DCE intersect in M, the Miguel point.

If ABCD is a cycle quadrilateral then E, F and M are collinear.