I is the incenter of ABC. We have CE = 12, AE = 9, and AB = 15. Find BC.
The length of BC is (15*12/9 =) 20.
Your answer is correct, but can you explain how you've done it? what's the logic behind that?
I can give a more detailed explanation.
Because BE is an angle bisector, we can use the angle bisector theorem. AB / BC = 9 / 12.
If AB = 15, so 15 / BC = 9 / 12
Thus, BC = 20.