+0

0
81
4
+887

Thanks :)

Jul 19, 2020

#1
+1193
+2

BY and CZ are angle bisectors, so by the angle bisector theorem, AZ/AC = BZ/BC and CY/BC = AY/AB. Plugging in some values from the givens gets us $$\frac{AZ}{AC} = \frac{8-AZ}{BC}$$ and $$\frac{4}{BC} = \frac{6}{8}$$, so BC = 16/3. Also note that AC = AY+CY = 6+4 = 10, so we have AZ/10 = 8-AZ/(16/3). Solving for AZ gets us 120/23, and since AB is 8, AB-AZ = BZ so BZ = 64/23.

You are very welcome!

:P

Jul 19, 2020
#3
+887
0

thanks!

qwertyzz  Jul 19, 2020
#2
+1326
0

Jul 19, 2020
#4
+2
0

64/23

Jul 19, 2020