Line BE and lineCF are angle bisectors of triangle ABC that meet at I as shown below, and we have CE = 4, AE = 6, and AB = 9. Find BC.
Important: The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
AE / AB = EC / BC
BC = (AB * EC) / AE