How to Find the Radius: A Beautiful Circle Geometry Problem

A Quick Break to Find the Radius

The workweek is in full swing — but if you’re looking for a moment to step away from the daily grind and recharge, here’s the perfect distraction: a clean, elegant geometry problem.

Find the radius!

The problem looks deceptively simple at first glance. Give it a try, and share your approach in the comments.

The Answer and Why It’s Worth Solving

The answer is 7 — and it comes out beautifully. That satisfying, clean result is exactly what makes this kind of circle geometry problem so rewarding to work through.

For a detailed step-by-step solution, check out the full walkthrough here.

Why Circle Geometry Problems Like This One Matter

Problems that ask you to find the radius from minimal given information are a staple of classical geometry. They train spatial reasoning, reinforce the relationships between chords, tangents, and inscribed angles, and often reward elegant thinking over brute-force calculation.

This one is no exception — and the clean integer answer is a hint that there’s a clever path to the solution.