Let ABC be a triangle, and let its angle bisectors be ¯AD,¯BE, and ¯CF, which intersect at I. If DI=3,BD=4, and BI=5, then compute the area of triangle ABC. (please include explanation if possible)
triangle BDI is a right triangle (sides are 3-4-5) That means that triangle ABC is isosceles, since the angle bisector AD is also an altitude. That means that BC = 2*BD = 8 AD is also a median of ABC, so AI = 2*DI = 6 The area of ABC is thus 6*8/2 = 24
