This is another problem from the Iowa State problem collection:

Looking for good math problems? The mathematics dept at Iowa State University has been asking its students weekly math problems for years. Here they are with solutions. https://t.co/KnsEquEtTJ

Tonight I tried another terrific (though very challenging) problem with my older son:

Here’s are his initial thoughts about the problem:

Now we rolled up our sleeves a bit and started to solve the problem. His first thought about what to do was to try to solve the problem with one inscribed circle and then with three inscribed circles:

The problem with three inscribed circles was giving him trouble so we moved on to a new movie and sort of started over on the three circle problem. While he was re-drawing the picture he was able to see how to make some progress:

Finally, having solved the problem with three circles, he moved on to solving the problem in general and found the surprising answer:

I really like these problems. Obviously not all of them are going to be accessible to kids, but the ones that are accessible are really amazing treasures!