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
- Solving quadratics
- 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.
See my website for the rest of this article