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.

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 two like this.

And with a bit of algebra, we find the radius of the circle.

How amazing 😊

What was your thought process this time? Comment down below, I am eager to know :) 💞

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Love, Bella ❤️