In triangle \(ABC, \)angle bisectors \(\overline{AD},\overline{BE},\) and \(\overline{CF}\) meet at \(I.\) If \(DI=3,\) \(BD=4,\) and \(BI=5\), then compute the area of triangle \(ABC.\)
I know that there are 2 more threads about this problem, but both these threads use Trignometry, and I want to use the Angle Bisector Theorem(I'm not trying to be picky, I just don't know Trig, yet!)
