 So this video we are going to practice working with measure of arcs versus arc length. And the first thing we're going to do is we have this picture of the circle over here and the first thing we're doing is finding the measure of arc AB. So here is AB, the arc, and remember the measure of that arc is always equal to its central angle. So angle AEB is a 90 degree angle, we can see that from the marking here. So the measure of arc AB is 90 degrees. Then what we're going to do next is find the circumference for circle E because remember to find arc length, and again notice when you're finding arc measure there's a little m. When you're finding arc length it's just the arc name. So in order to find arc length remember we're going to use that formula that involves circumference. So we need to find the circumference of circle E. As they tell us the radius is 6, to find the circumference I'm going to do 2 times pi times r, which r the radius is 6, and so that's going to equal 12 pi. I'm not going to evaluate that, I'm just going to leave it in terms of pi. So 12 pi is the circumference. Now when I come down here to find arc length I have to use that little formula. So remember the formula is the measure of the arc over 360 degrees multiplied by the circumference of the circle. So we know what the measure of the arc is. We said up here that it's 90 degrees so we're going to do 90 over 360 times 12 pi. And what I like to do is because this is a fraction I'm going to make this a fraction just by putting it over 1. Now what I'm going to do is just simplify this fraction. So 90 over 360 because they both end in zeros first thing I can do is cancel out those zeros. So now I'm really dealing with the fraction of 9 over 36. So how do we reduce 9 over 36? Hopefully you are saying to yourself 9 goes into 9 once and 9 goes into 36 four times. So I have 1 fourth times 12 pi and to multiply fractions you go straight across. So 1 times 12 pi and 4 times 1. And then once again you can reduce 12 over 4 and we get 3 pi. So what we're looking at here is the measure of the arc. So the measure of arc AB is 90 degrees but the length of arc AB if I was going to walk from A to B the length is 3 pi. In this example we're going to find the measure of arc ABC to start with. And so when I look at the picture ABC right away hopefully you're recognizing that's a semi-circle. So the measure of arc ABC is 180 degrees. And so now I'm going to use that to find arc length. I want to know that the length of arc ABC. So I'm going to use the formula 180 because that's the measure of the arc over 360 multiplied by the circumference and remember in the last video we found the circumference is 12 pi. So now I'm just going to go ahead and reduce 180 over 360 I can reduce by 10 so get rid of the zeros. And now I'm dealing with 18 over 36 which hopefully you recognize is one half. You can multiply that by 12 pi. You get 12 pi over 2 which is 6 pi. So if I was going to walk from A to C if I was going to walk halfway around the circle I would be walking 6 pi units. I'm just noticing that this one's asking us to do measure of arc AB and arc length of AB and we already did that. So if you just look back a couple of slides earlier than this you will find that the measure of arc AB is 90 degrees and we figured out that arc length was 3 pi. Okay the measure of arc CD so now we're looking at this arc right here CD we can see that the central angle is 30 degrees so the measure of that arc is 30 degrees and then we'll use that to help us in the formula for finding arc length. So the measure of arc CD is 30 over 360 times circumference which is remember 12 pi and if I reduce again I'm going to reduce by 10 to get rid of those zeros and 3 over 36 is 1 over 12 and since I'm multiplying by 12 pi what's going to end up happening is those 12s 12 pi over 12 will cancel each other out and I'm left with pi so the length of arc CD would be equal to pi the measure of arc AD so now we're looking at this arc right here measure of that arc is equal to its central angle of 150 degrees so to find the length of arc AD we're going to take that measure 150 over 360 multiply by 12 pi because that's the circumference and go ahead and reduce so reduce by 10 we get rid of those zeros and what goes into both 15 and 36 I would say 3 3 goes into 15 5 times 3 goes into 36 12 times and then we multiply by 12 pi so before you multiply you might recognize here before we multiply straight across the 12s can cancel each other out and we are just left with 5 pi so the arc length from A to D would be 5 pi units