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Current time:0:00Total duration:5:27

CCSS.Math:

what I want to talk about in this video is the notion of Arc measure when we're dealing with circles and as we'll see sometimes when you see something like arc measure you might think it's the length of an arc but arc length is actually a different idea so we will compare these two things arc length to arc measure so arc measure all that is it's just a fancy way of saying if I have a circle right over here this is my best attempt at drawing a circle I have a circle here the center of the circle let's call that point O and let me put some other points over here so let's say that this is point a let's say this is point B and let's say this is point C right over here and let's say that I have that let's say the central the central angle right over here because it includes the center of the circle so the central angle angle AOB let's say it has a measure of let's say it has a measure of 120 degrees and if someone were to say what is the measure of Arc a B so let me write that down the measure so if someone were to say what is the measure of Arc a B and they'd write it like this so that's referring to arc a B right over here it's the minor arc so there's two ways to connect a B you could go you could connect it right over here this is the shorter distance or you can go the other way around which would be which would consider the major arc now if someone's referring to the major arc they would say mark ACB so when you're given just two letters you assume it's the shortest distance between the two you assume and that it is the minor arc in order to specify the major arc you would give the third letter to go the long way around so the measure of my arc a B and sometimes you'll see with the parentheses right over here all this is this is the same thing as the measure of the central angle that intercepts that arc well the central angle that intercepts that arc has a measure of 120 degrees so this is just going to be 120 degrees now some of you all might be saying well what about the major arc well let's write that so if we're talking about arc a C B so we're going the other way around so this is the major arc so what is the measure of Arc a C B once again we're using three letters so that we're specifying the major arc well this angle this central angle right over here to go all the way around the circle is 360 degrees so this is going to be the 360 minus the 120 that we're not including so 360 degrees minus 120 is going to be is going to be 240 degrees so the measure of this of this angle right over here is 240 degrees so the arc the the length the measure of this arc have to be careful not to say length of that arc the measure of this arc is going to be the same as the measure of the central angle it's going to be 240 degrees now this is going to be the case these are these are measures are going to be the case regardless of the size of the circle and that's where the difference starts to be from arc measure to arc length so I could have I could have two circles so this circle right over here and that circle right over here and as long as the central angle that intercepts the arc has the same degree measure so let's say that that degree measure is the same is the same as these are central angles so we're assuming the vertex of the angle is the center of the circle as long as these two are the same these two central angles have the same degree measure then the arc measures then the corresponding arc measures are going to be the same but clearly these two arc lengths are different the arc length is not going to depend only on the measure of the central angle the arc length is going to depend on the size of the actual circle arc measure is only dependent on the measure of the central angle that enters peps that ark so your maximum arc measure is going to be 360 degrees your minimum arc measure is going to be zero degrees it's measured in degrees not in units of length that arc length would be would be measured in so let me write this down this only depends so this is what's going to drive this is the measure measure of central angle central angle that intercepts the arc that intercepts intercepts the arc when you talk about arc length yes it's going to be dependent on the angle but it's also dependent it's going to be dependent on the measure of that central angle plus the size of the circle size of the circle you're actually talking about a length now when you talk about arc length well here you're talking about a degree measure