What do the arcs of a circle add up to

Finding arc measures with equations. Practice: Arc measure with equations. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Voiceover] What I want to talk about in this video, is the notion of Arc Measure, when we're dealing with circles.

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 is 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, let's say the central angle, right over here, cause it includes the center of the circle, so the central angle, angle AOB.

Let's say it has a measure of degrees. And if someone were to say, what is the measure of arc AB? So, let me write that down. The measure. So, if someone were to say what is the measure of arc AB, and they'd write it like this, so that's referring to arc AB right over here. It's the minor arc, so there's two ways to connect AB, you could connect it right over here, this is the shorter distance, or you can go the other way around, which would be what you'd consider the major arc.

The vertex is the center of the circle. An arc of a circle is a continuous portion of the circle. It consists of two endpoints and all the points on the circle between these endpoints. The symbol is used to denote an arc. This symbol is written over the endpoints that form the arc. There are three types of arcs:. In Figure 2 , AC is a diameter. In Figure 3 , is a minor arc of circle P. In Figure 4 , is a major arc of circle Q.

Arcs are measured in three different ways. They are measured in degrees and in unit length as follows:. Every pair of endpoints defines two arcs. An arc whose measure is less than degrees is called a minor arc. An arc whose measure is greater than degrees is called a major arc. An arc whose measure equals degrees is called a semicircle, since it divides the circle in two. Every pair of endpoints on a circle either defines one minor arc and one major arc, or two semicircles.

Only when the endpoints are endpoints of a diameter is the circle divided into semicircles. From this point on, unless otherwise mentioned, when arcs are discussed you may assume the arc is a minor arc.

A central angle is an angle whose vertex is the center of a circle. Any central angle intercepts the circle at two points, thus defining an arc. The measure of a central angle and the arc it defines are congruent. A chord is a segment whose endpoints are on a circle. Thus, a diameter is a special chord that includes the center. Chords have a number of interesting properties.

Every chord defines an arc whose endpoints are the same as those of the chord.