In triangle ABC, AB = 6, BC = 4, and AC = 5. The angle bisector of angle B meets AC at P. Find CP.
+23245 The angle bisector divides the side in the same proportion as the other two sides of the triangle.
So: BC : AB = CP : PA
If CP = x, then PA = 5 - x.
---> 4 : 6 = x : 5 - x
4 / 6 = x / (5 - x)
4·(5 - x) = 6·x
20 - 4x = 6x
20 = 10x
x = 2 ---> CP = 2
5 - x = 3 ---> PA = 3
