PUMaC 2014 Team Problem 11

\triangle A B C has A B=4 and A C=6. Let point D be on line A B so that A is between B and D. Let the angle bisector of \angle B A C intersect line B C at E, and let the angle bisector of D A C intersect line B C at F. Given that A E=A F, find the square of the circumcircle’s radius’ length.