 This video goes over some more important vocabulary that has to do with circles. We're going to start with the first one here, which is central angle. This is a really important concept. A central angle is an angle whose vertex is the center of a circle. So if I'm looking at this picture, B is the center of this circle, which means when I write down a central angle, I have to make sure that B is in the middle of the three letters because it's the vertex. So for example, angle A, B, D is considered a central angle. The vertex is the center of that circle. Another example of a central angle would be angle C, B, D. You could write down other examples. For example, angle A, B, C, that is considered a central angle. And you could say it the other way too, angle C, B, A. And let's see, I think we have, oh, one other one would be angle D, B, A, or A, B, D. Oh, I already wrote that one down. So you can see that there's two ways to write that same angle, angle A, B, D, or D, B, A. A minor arc is an arc whose central angle is, and here's where you want to fill in the blank, a minor arc is an arc whose central angle is less than 180 degrees. So a minor arc would be an arc, and arc is this part. Okay, the angle is this part in here, and the arc is this distance out here. So for example, you'll notice that minor arcs are named by the letters of the two end points. So if I take this central angle, A, B, D, it has a minor arc of D, A, or AD. And the way that you write that is, and again, it doesn't matter the order AD or DA, and you put an arc over it. Another example would be using this central angle, C, B, D, the arc C, D. So another example would be the arc C, D. So minor arc has two letters, and the central angle of that arc has to be less than 180 degrees. Hopefully we're all familiar with a semi-circle. Semi-circle is just an arc whose end points are the end points of a diameter. Its central angle is equal to 180 degrees. So a semi-circle in this picture if I look at the diameter is AC, I have two semi-circles, either the one up here, which is AC, or the one down here, which is also AC. And that's why this part is so important. It's named by the letters of the two end points, so A and C, but you also have to include another point on the arc. So if I'm going to name the semi-circle, it's going to be ADC or I would have to add another point. If I wanted to name this semi-circle, it's up here. I would have to add a point. Let's just call that F. And so that would be called semi-circle AC. And again, notice how you put the arc over those letters. A major arc is an arc whose central angle is bigger than 180 degrees. So remember a minor arc has to be smaller than 180 degrees. So it has to be smaller than a semi-circle. A major arc has to be bigger than a semi-circle. It has to be bigger than 180 degrees. And it's important again to notice here that when we name a major arc, you have to use three letters. You have to use the letters of the two end points and another point on the arc. Okay, so if I'm going to name a major arc from this picture up here, for example, I would say arc DCA. DCA is a major arc because you'll notice that you start here at D, go through the point C, all the way around to A. That's bigger than a semi-circle, so that would be considered a major arc. Using the points that are already on that circle, that's really the only major arc that we see. If I use this point F that I kind of added before, then I could write down some other major arcs. For example, I could say DAF, that would be a major arc. So endpoint D goes through A, stops at F. That's a major arc because it's bigger than a semi-circle. The other important thing to notice is this statement here, the sum of the measures of, sorry, the central angles of a circle with no interior points in common is 360 degrees. What that means is if you look at a circle, if you add up all the central angles, it should always total 360 degrees. And that's why a semi-circle, when you cut it in half, that central angle is 180 degrees. So all the way around is 360, half or semi-circle is 180 degrees. Okay, this is the last part of this video, and it's the most important. We're going to talk about the difference between a measure of an arc and arc length. So we've been introduced to what an arc is. So for example, CD is an arc. Well, CD has two measurements. It has a measure and it has a length. So we need to talk about the difference between measure of an arc and arc length. Measure of an arc is equal to its central angle. Okay, so if I'm talking about arc CD, for example, the measure, and I have to put a little M in front of that because I'm telling the measure of arc CD is going to be 30 degrees. Because CBD is the central angle, and we can see that that's 30 degrees, the measure of arc CD is equal to that. So the measure of this arc is considered 30 degrees. Now, when we talk about arc length, we're talking about literally how far is it from C to D. If we were walking this circle, if we started at C and stopped at D, how many inches or feet or miles would we be walking? So arc length is actually a formula. What you have to do is you have to take the measure of the arc, so hard to write on this, the measure of the arc over 360 degrees, okay, and then you're going to multiply that by the circumference of the circle. So what you're doing is you're taking, for example, this 30 degrees, you're going to do 30 over 360 because that's giving you just this portion of the circle, and then multiply it by the circumference because you're not walking all the way around the circle, you're just going from D to C or C to D. So measure of the arc is always a degree, and you have to use this little M, arc length is always a unit value like inches or centimeters or feet or miles, and you have to use this formula. So you're going to get some practice in the next video of finding measure of an arc versus arc length.