WEBVTT

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- [Voiceover] What I want
to talk about in this video,

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is the notion of Arc Measure,

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when we're dealing with circles.

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As we'll see, sometimes when you see

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something like arc measure,

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you might think it's the length of an arc,

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but arc length is
actually a different idea.

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So we will compare these two things.

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Arc length to arc measure.

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So arc measure, all that is

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is just a fancy way of saying,

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if I have a circle right over here,

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this is my best attempt
at drawing a circle.

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I have a circle here.

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The center of the circle,
let's call that point O,

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and let me put some
other points over here.

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So let's say that this is point A,

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let's say this is point B,

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and let's say this is
point C right over here.

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And let's say that I have,

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let's say the central
angle, right over here,

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cause it includes the
center of the circle,

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so the central angle, angle AOB.

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Let's say it has a measure of 120 degrees.

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And if someone were to say,

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what is the measure of arc AB?

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So, let me write that down.

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The measure.

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So, if someone were to say
what is the measure of arc AB,

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and they'd write it like this,

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so that's referring to
arc AB right over here.

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It's the minor arc, so there's
two ways to connect AB,

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you could connect it right over here,

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this is the shorter distance,

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or you can go the other way around,

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which would be what you'd
consider the major arc.

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Now, if someone's
referring to the major arc,

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they would say mark ACB.

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So when you're given just two letters,

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you assume it's the shortest
distance between the two.

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You assume that it is the minor arc.

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In order to specify the major arc,

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you would give the third letter,

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to go the long way around.

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So the measure of arc AB, and sometimes

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you'll see it with
parenthesis right over here,

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all this is, this is the
same thing as the measure

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of the central angle
that intercepts that arc.

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Well, the central angle
that intercepts that arc

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has a measure of 120 degrees.

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So this is just going to be 120 degrees.

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Now, some of y'all might be saying,

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well, what about the major arc?

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Well, let's write that.

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So if we're talking about arc ACB,

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so we're going the other way around,

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so this is major arc.

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So what is the measure of arc ACB,

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once again we're using three letters,

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so that we're specifying the major arc.

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Well, this angle, this
central angle right over here,

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to go all the way around
the circle is 360 degrees.

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So this is going to be
the 360 minus the 120

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that we're not including.

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So 360 degrees minus 120 is going to be,

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is going to be 240 degrees.

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So the measure of this angle
right over here is 240 degrees,

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so the measure of this arc,

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I have to be careful not
to say length of that arc,

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the measure of this arc
is going to be the same

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as the measure of the central angle.

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It's going to be 240 degrees.

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These arc measures are
going to be the case

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regardless of the size of the circle,

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and that's where the
difference starts to be

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from arc measure to arc length.

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So, I could have two circles,

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so this circle right over here

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and that circle right over here,

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and as long as the central
angle that intercepts the arc

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has the same degree measure,

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so let's say that that degree
measure is the same as,

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these are central angles,

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so we're assuming the vertex of the angle

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is the center of the circle.

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As long as these two are the same,

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these two central angles
have the same degree measure,

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then the arc measures, then
the corresponding arc measures

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are going to be the same.

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But clearly, these two
arc lengths are different.

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The arc length is not going to depend

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only on the measure of the central angle,

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the arc length is going to depend

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on the size of the actual circle.

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Arc measure is only dependent

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on the measure of the central angle

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that intercepts that arc.

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So your maximum arc measure
is going to be 360 degrees.

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Your minimum arc measure is
going to be zero degrees.

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It's measured in degrees,
not in units of length

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that arc length would be measured in.

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So, let me write this down.

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This only depends...

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So, this is what's going to drive this

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is the measure of central
angle, central angle,

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that intercepts the arc.

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That intercepts, intercepts the arc.

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When you talk about arc length,

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yes, it's going to be
dependent on the angle,

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but it's also dependent,
it's going to be dependent

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on the measure of that central angle

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plus the size of the circle.

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Size of the circle.

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You're actually talking
about a length now,

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when you're talking about arc length.

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While here, you're talking
about a degree measure.