 Welcome to Chapter 10. In this video, we are going to introduce you to some vocabulary dealing with circles. So, in this slide, the first thing that we want to do is understand how to name a circle. You see over here, obviously, you have a picture of a circle. And when you name a circle, you always use the center point. So we would call this circle, circle C. So you always name your circle based on the center point. Next thing we have here, number two, what is a radius? A radius is the segment that connects the center point to any point on the circle. So you can see in this picture, C going to A would be considered a radius, or C going to B would be considered a radius. So first, let's write down the definition of what is a radius. It is a segment that connects the center of the circle to any point on the circle. And if we want to name a radius, all we have to do is use the center point and the segment end point, which is on the circle. So, for example, C A would be a radius, C B would be a radius, C D would also be a radius. Any of those would be acceptable. Number four, what is a diameter? Well, a diameter is related to a radius. A diameter is instead of connecting the center to a point on the circle, it is the segment that connects one point on a circle to another point on the circle, but it has to go through the center. So what is a diameter? Diameter is the segment that connects two points on a circle through the center. So that's the really important point is that you have to go through the circle if you are dealing with the diameter. So if we want to name a diameter from this picture, there's only one being shown on this picture and that is A to D. And you can see it's going right through the center, so A D would be considered a diameter. Number six, if the diameter of the circle is 15, what is the radius? Well, if you pay attention to the relationship between radius and diameter, you can take a look at this picture and you see that AC, which is a radius, is exactly halfway from A to D. So AC, the radius, is always half of the diameter. Or, you can think of it the other way, a diameter, A D, is always two times a radius. So if you take CD and multiply by two, you're going to get the diameter, which is A D. So if the diameter is 15, in order to get the radius, we would have to do 15 divided by two. And so that would be 7.5. So you want to make sure that you keep in mind that diameter is always two times the radius and that radius is always diameter divided by two. Number seven, what is circumference? Well, circumference is the distance around a circle. So for example, if I start at A and I travel all the way around the circle and get back to A, that distance is considered the circumference. So we probably know that as perimeter. But when it's a circle, we don't use the word perimeter. We use circumference. So what is circumference? It is perimeter of a circle. It is the distance around the circle. And the formula for circumference has to do with radius or diameter. There's actually two formulas that you can use. And so we're going to write both of them down. Capital C is what we use for circumference. And there's two ways to find circumference. You can either do pi times diameter or you can do two times pi times radius. So it's all dependent upon what you know. We already talked about the fact that if you know diameter, you can always figure out radius. If you know radius, you can always figure out diameter. So really, whether you use this formula or this formula, it really doesn't matter. You should be able to figure out circumference, whether you're given radius or diameter.