# Making Fun Algebra Problems Funner

A month ago, a friend posted the following problem on Facebook. I just noticed it this week.

The goal is to find the exact length of the radius .

I love this kind of math problem. It has a bunch of features that make it a great, toy math problem.

• It looks like it’s going to be easy, but at the same time seems at a glance to not have enough information
• It looks like a geometry problem but only requires that you know:
• All radii of a circle have the same length
• A radius to a point where a tangent line touches the circle is perpendicular to that tangent line
• It requires only very basic algebra:
• Pythagorean theorem
• The numbers in the problem are small, non-zero integers

I spent the next 25 minutes and six pieces of paper working the problem. About 20% of the time that I spent was rechecking my work. Why did I bother rechecking my work on a toy problem?

Warning: Spoilers ahead. If you like this kind of problem, stop reading now and play with it first.