In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.
https://web2.0calc.com/questions/in-triangle-abc-let-the-angle-bisectors-be-by-and_1
Very similar question here! The numbers are just changed a bit, but it was answered well!
I hope this helps you!
Thanks! :)