Working through a neat circle / rectangle puzzle from Catriona Agg

Earlier this week I saw a really neat puzzle from Catriona Agg:



We’ve done lots of projects with Catriona’s puzzles in the past, so just search for “Catriona” and you’ll find them.

My younger son spent some time off camera solving the puzzle and then I asked him to walk through his solution. His solution gets the main idea about tangents and circles, and then computes the radius of the semicircles using the Pythagorean theorem:



Typically when we play with one of Catriona’s puzzles I have my son look through the twitter thread afterwards and find a neat solution. I took a different approach today and showed him how to use similar triangles to get to the answer with slightly less computation:



I really like Catriona’s puzzle. I also think that my son’s explanation is a great example of what kids doing math looks like.