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?

Kudos, Straight!

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.

Thanks, proyaop!