There is a triangle $ABC$. A line bisects the angle at the vertex $A$ and cuts the side $BC$ in point $D$ such that $BD=9$ and $DC=12$. If $O$ is the center of the circle that is inscribed inside the triangle $ABC$ and $AO:OD=4:3$, find the perimeter of the triangle $ABC$.
This seems very hard to me.
edit: I even drew one bad picture of this problem: