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.

mrinank Sep 27, 2022

#1**+1 **

Use the angle bisector theorem! Set AZ = x and BZ = 8 - x. Can you use this theorem from here?

Voldemort Sep 28, 2022

#2**+3 **

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**

proyaop Sep 28, 2022