Circles are simple, but they do have parts. One part is an arc, a snippet of the circle, a piece of its circumference. Arcs themselves come in types, like major arcs, semicircles, and minor arcs.

A circle is the set of all points equidistant from a given point. **Circumference** is the distance around a circle.

*[insert drawing of circle with curved arrow going around it to show circumference]*

Circles can have angles created by two radii. These are **central angles** and are almost always designated using either their exact angle (or radian) measurement or the Greek letter theta, ϴ:

*[insert circle drawing with central angle ϴ]*

Circles can also have angles created by two chords (line segments with endpoints on the circle) with a common endpoint on the circle. These angles are called **inscribed angles**:

*[insert drawing of inscribed angle]*

Both central angles and inscribed angles create major and minor arcs.

An **arc** is a portion of a circle that is less than the entire circle. Since that allows nearly all possible portions, mathematicians break down arcs like this:

**Minor arc**-- An arc measuring less than or equal to 180° or π radians**Semicircle**-- An arc measuring exactly 180° or π radians, which excludes designating either part of the circle as major or minor**Major arc**-- An arc measuring greater than or equal to 180° or π radians

*[Insert two drawings -- one of a circle divided into a minor arc and major arc, the other drawing showing a circle divided into two semicircles]*

In a typical drawing of a circle, the reader understands the minor arc to be the one under discussion. In this drawing, we care about the minor arc identified by the central angle ϴ:

*[insert drawing of circle with central angle ϴ creating an acute angle, with the minor arc of that angle emphasized]*

Labeling a minor arc requires only its endpoints on the circle. Here is minor arc GO:

*[insert drawing of circle with minor arc GO labeled and emphasized]*

If you want the major arc, select and label both endpoints of the arc and a random point between. Here we have major arc FUN:

*[insert drawing of circle with three points F, U, N on the major arc]*

Arcs are usually identified in writing using their points (two for a minor arc, three for a major arc) and then drawing a tiny, short arc drawn over the letters:

Arcs have two measurements:

- Angle
- Length

One way to measure an arc is by the central angle of the circle. This is the **arc angle**. You place a lowercase m in front of the written form for the arc, like this:

So you could write mFUN = 45°, and you would say, "The major arc FUN measures 45 degrees."

The other way to measure arcs is by their distance along the circumference of the circle. This is the **arc length**. To write arc length in words, you put a small l in front of the written form, like this:

*[refer to Figure 2 emailed, and put graphic arc above lGO below]*

So you could write lGO = 13.4 cm and you would say, "The length of arc GO is 13.4 centimeters."

Instructor: **Malcolm M.**

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

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