In the triangle ABC, $MN \parallel BC$, $BO$ and $CO$ are angle bisectors of $\angle MBC$ and $\angle NCB$ respectively. If $AB=12$, $BC=24$ and $AC=18$, then what is the perimeter of $\triangle AMN$ ?
I made an aproximated drawing
I tried with similarity but got nothing there. Maybe i'm not seeing the similar triangles in the correct way. Any hints in this kind of problem?