HMMT 2014 G3

$A B C$ is a triangle such that $B C=10, C A=12$. Let $M$ be the midpoint of side $A C$. Given that $B M$ is parallel to the external bisector of $\angle A$, find area of triangle $A B C$. (Lines $A B$ and $A C$ form two angles, one of which is $\angle B A C$. The external bisector of $\angle A$ is the line that bisects the other angle.)