Two circles O1 and O2 intersect each other at M and N. The common tangent to two circles nearer to M touch O1 and O2 at A and B respectively. Let C and D be the reflection of A and B respectively with respect to M. The circumcircle of the triangle DCM intersect circles O1 and O2 respectively at points E and F (both distinct from M). Show that the circumcircles of triangles MEF and NEF have same radius length. geometrygeometric transformationreflectioncircumcirclerotationtrapezoidtrigonometry