A nice AMC 10 angle bisector problem

I love how the AMC 10 problems combine multiple ideas. A problem from the 2010 AMC 10 a gave my son some trouble today because he didn’t understand one of the words and also because he needed a little review with the angle bisector theorem. It made for a good morning math talk. Here’s the problem:

 

We started off talking about the problem to understand what “nondegenerate” meant also ended up getting to a point where the Angle Bisector Theorem was the stumbling block:

Since the Angle Bisector Theorem was the stumbling block – we took a short detour to review that theorem:

Following that short review (and unfortunately it had to be short since he needed to get out the door to go to school) we revisited the problem:

So, another great AMC 10 problem. I love how these problems combine different concepts and highlight areas to review. I’d never be able to make up problems like this one on my own.