1983 AHSME Problems/Problem 19
Point is on side of triangle . If , then the length of is
Let . Since bisects , the Angle Bisector Theorem gives , so write and . Applying the Law of Cosines to gives , and to gives . Subtracting times the first equation from the second equation therefore yields , so is or . But since ( is the length of a side of a triangle), must be , so the answer is .