What a kid learning math can look like – incircles and circumcircles

This problem gave my son a lot of trouble this morning. It is from one of the challenge problem sections in Art of Problem Solving’s Introduction to Geometry book:

A triangle has side lengths of 10, 0, and 12, find the lengths of the radius of the inscribed and circumscribed circles.

This problem looks like a pretty plain vanilla math contest problem, but he’s not studying for math contests. He drew an amazing picture of the situation:

After talking about the problem a bit this morning we moved on to other things. When he got home from school we revisited it. Here are his thoughts on the incircle part of the problem:

Here are his thoughts on the circumcircle part of the problem:

Finally – and unfortunately interrupted by a phone call – here’s his explanation of how the project from today relates to a 3d printing project that we’d done previously

Definitely a fun problem to talk through, and really nice to see that he was able to explain the ideas in a problem that he’d really struggled with in the morning.