In triangle ABC angle bisectors AD, BE, and CF meet at I. If DI = 3, BD = 3*sqrt(3), and BI = 6, then compute the area of triangle ABC.
Triangle ABC is an isosceles triangle with the base of 8 units.
angle (B) = 2(arctan3/4)
angle (A/2) = 90 - angle (B)
height AD = BD / tan(A/2)
area = BD * AD = 54.85714289 units squared