Question 66
Circles $O_1,O_2$ intersect at $M,N$. Their common external tangent nearer $M$ touches them at $A,B$, respectively. Let $C,D$ be the reflections of $A,B$ in $M$. The circumcircle of $DCM$ meets $O_1,O_2$ again at $E,F$, respectively. Prove that triangles $MEF$ and $NEF$ have equal circumradii.
