Mathematics & Geometry

Are You Smart Enough To Find The Radius?

A Fun Geometry Challenge

We want to find the radius of the circle. This is a very nice puzzle as anyone with some knowledge of high school geometry and some creativity can solve!

Here’s a hint: draw some lines …

I recommend you to pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for the solution! ✒️

Solution

We first denote the radius of the circle as r.

We can extract further information from the given figure by drawing a diagonal in the little 2 by 2 square.

To find the length of the diagonal, we use the Pythagoras’ Theorem.

Since this is a 4 by 4 square, the diagonal of the big square is simply double that of the diagonal in the smaller square, which is 4root2.

That means the diameter of the circle is just a tad bit less than 2root2.

So how do we find the radius? The key is to construct a smaller square of side r around the upper right corner.

like this

We can again use Pythagoras’ Theorem to find the length of the diagonal in the r by r square.

Let’s put this onto the diagram.

Now the big diagonal is always equal to itself. We previously found that its length is 4root2. And so we can equate the…