Let ABC be an acute triangle ( AB < AC ) inscribed in a circle with center O; E is the midpoint of minor arc BC. Let M be the point on side AC such that EM = EB ( M is different from C ); N is the intersection of BM with the circle with center O ( N different from B ). Let I be the intersection of BM with AE; K is the intersection of AC with EN. Prove that quadrilateral EKMI is a cyclic quadrilateral.