Congruence problem $BF = FC$

Question

We have an $ABC$ triangle in which $\angle ABD=\angle ACB,AB=12,AD=8,BC=15,DF\perp BC$.How to show that $[BF]\equiv[FC]$

I did a figure in geogebra but i don't see what triangles are similar i know that one angle is equal if I knew $BD=?$ I could show that $ABD$ and $ACD$ triangles are similar from side-angle-side

Answer 1

Hints towards a solution. If you're stuck, show what you've tried.

1. Show that $ABD, ACB$ are similar triangles.
2. Hence calculate $DC$.
3. Hence show $BD$ is an angle bisector.
4. Hence $BDC$ is an isosceles triangle, and $BF = FC$.