In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BC.

By the angle bisector theorem, BC = 13/3.

 In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BC.

Angle  Bisector Theorem

BC / CY = BA / AY

BC / 3 = 8 / 6

BC  =  3 * 8 /  6  =    24 / 6   =   4

 In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BZ.

In the other problem we found that BC = 4

So, again, by the angle bisector theorem

AC / BC = AZ / BZ

9 / 4  =  AZ / BZ

So....there  are 13 parts to AB

And BZ  =  4 of them

So

BZ =  (4/13)(AB)  =  (4/13)(8) =   32/ 13

CORRECTED  !!!