In this video, I'm going to show you how to find the centre of a circle. So, there's two ways of finding the centre of a circle. The first way is by drawing it. The second way is by using the equations. So, first, I'll start with how to draw it. See here, we have a circle and basically, the easiest way is you put one end of a ruler on the circle and then, you swing the ruler around like this. Keep this point here at zero and you find the longest length on the circle. See here, I'm at ten inches here. When I swing around to here at ten again, so that's not the longest. The longest point here is this one here, which is eleven inches across, okay. So, that there is called the diameter of the circle and basically, it moves the longest length of the circle and passes through the centre. For the moment, we don't know where the centre is on this line so what we need to do is exactly the same thing from any other point on the circle. So, let's take this point. We swing the ruler around like this. Find the longest point again. It's there. Draw the line. Now, where these two cross, that's another diameter of the circle. Where these two points cross there, that's the centre of the circle. That's one way using the graph - graphically showing it. There's another way - using the equation. The equation of a circle looks complicated but it isn't. It looks like this: x minus a squared plus y minus b squared equals r squared. Now, this is simple enough. It says that a, b and r, that's the only letters you need to know. R represents the radius of the circle, which is from here to the edge, from the centre to the edge, and the centre of the circle here is simply the point a, b written in coordinates, so this point, a, b. So, you could have the equation of the circle looking like this: x minus two squared plus y minus three squared equals nine. So, here you can see that a is two and b is three so that means that the centre of the circle is the point a, b. That's equal to two, three. A is two and b is three, okay, and r squared represents nine so r squared is nine so the radius is three. And that's how to find the centre of a circle. .

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