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 $ABC.$
already did this one
Since the sides of triangle DBI are 3,4,5 it is a right triangle.
So AD is also an altitude
So ABC is isosceles
DI is 1/3 the altitude, so AD = 6
The area is 1/2 * 6 * 8 = 24