+30 In triangle ABC let the angle bisectors be segment BY and CZ . Given AB = 8, AY = 6, and CY = 3, find BZ, I found BC, but I need further help with BZ.
+289 Use the angle bisector theorem! Set AZ = x and BZ = 8 - x. Can you use this theorem from here?
+1632 Just to clarify @mrinank, the angle bisector theorem is thus:
BC/AB = CY/AY
Then you get BC.
Then you do angle bisector theorem again, use BZ as x, and AZ as 8-x. Apply angle bisector theorem, AC/BC = AZ/BZ = (8-x)/x.
To solve: BC = 4. 9/4 = (8-x)/x => 9x = 32 - 4x, 13x = 32, x = 32/13 = BZ
