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How to Find the Center of a Circle (and Save Christmas)

Ever needed to find the center of a circle? It’s one of those things that seems easy - until you have to do it. But rest assured there is a trick to figuiring it out, and it's indeed fairly simple. Keep on reading for Math Dude's quick and easy method!

By
Jason Marshall, PhD,
Episode #223

Pumpkin PieHave you ever noticed that cutting pie, cake, pizza, or anything else that’s round is hard work? Unless you’re really careful, that all-important first cut tends to miss the center of the circle. And that can be a serious slip-up, because it throws everything from that point forward totally out of whack.

Case in point: The Math Dude Thanksgiving gathering of 2014.

The perpetrator? Let's call him “Bob," to protect his identity. The weapon? An ordinary kitchen knife. The accused crime? Butchering the all-important first cut of the achingly beautiful, feast-topping pumpkin pie. The verdict? Guilty of doling out huge wedges of delicious pie to approximately half the gathering, and sadly-small slivers to the rest—including one "Math Dude."

Today, we’re going to talk about how you can avoid this mishap and save yourself from future holiday misfortunes. What’s the secret? It all comes down to finding the exact center of a circle. And that, math fans, is precisely what we’re going to learn how to do today..

How to Find the Center of a Circle

Finding the center of a circle is one of those things that seems like it should be really easy to do - until you’re faced with the problem of doing it. Sure, you could just stab out a guess at where the center is, but that’s how “Bob” got in trouble cutting the pie in the first place, remember? Which means there must be a better way to do it.

Actually, there are a number of relatively simple ways to find the center of a circle. Before we get to pies, let’s think about finding the center of a circle you’ve drawn on a sheet of paper. Of course, if you were to draw a circle on a sheet of paper, you’d probably use a compass—which means you’d already know the location of the circle’s center. But let’s pretend you don’t already know it, and let’s think about what you could do to find it.

Method #1: Circumscribe a Square

Our first method begins by drawing a square around the circle. Technically, this is called circumscribing the circle with a square—which is just a fancy way of saying that we draw a square so that each of its four sides just touches the circle.

Square Circumscribed Around Circle

Of course, the tricky part of doing this is making sure that the square is actually a square - in other words, making sure that each of its four angles are right angles. One way to do this is to use the 3-4-5 triangle method that Knot Dude used when helping his ancient Egyptian father, Papa Knot, build the foundation for the Great Pyramid. What, you’ve never heard that story? Then you need to check out the Math Dude episode called Why Is Algebra Useful?

Once you’ve used Knot Dude's method and have a ship-shape square circumscribed around your circle, all you have to do is draw a straight line from the top-left corner of the square to the bottom-right corner, and from the top-right corner to the bottom-left. The point at which these two diagonal lines intersect is the center of the square. And it’s also the center of the circle.

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