Triangle geometry with bisectors

Question

In triangle $ABC$, $AB=10$, $CA=12$. The bisector of ∠B intersects $CA$ at $E$, and the bisector of ∠C intersects $AB$ at $D$.

$AM$ and $AN$ are the perpendiculars to $CD$ and $BE$ respectively. If $MN=4$, then how can I find $BC$?

Thank you!