## A theorem of two intersecting circles or two adjacent isosceles triangles(An application of a generalization of Van Aubel's Theorem)

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The following intriguing problem was circulated by Dick Klingens at the annual meeting of the Nederlandse Vereniging van Wiskundeleraren (NVvW) in November 2011:
Two circles K1 and K2 intersect each other in B and Q. A line through Q cuts K1 in point A and K2 in point C. The points E and F are the respective midpoints of the arcs BA and BC that do not contain Q. If M is the midpoint of AC, prove that ∠EMF = 90o

A different, but equivalent formulation of the same problem is the following:
Given two isosceles triangles ABC and BDE with respective bases AB and BD lying in a straight line (and on the same side of the line), and BC is perpendicular to BE. If M is the midpoint of AD, prove that ∠CME = 90o.