I wanted to start the year off with this, until I realized (duh) that it really uses the Pythagorean Theorem.
But it’s a great problem, and so rich for spinning off. What about triangles? What about pentagons? What about irregular triangles? Can you always gets a circle around the polygon, no matter where you start? (An honest-to-god context for drawing a circle through three points.)
More than ever, I’d like to really focus on problem posing this year, and this problem is very rich for jumping off from. I love it, and can’t wait to bring it in to class.