7-6 Circles and Arcs, Part 1

L.E.Q. How do you find the measures of central angles and arcs?

Central Angles and Arcs

A circle is the set of all points equidistant from a given point called the center.

You name a circle by its center. The circle below is named “circle P”.

What is a Circle?

Radius - a segment that has one endpoint at the center and the other endpoint on the circle.

Diameter - a segment that contains the center of a circle and has both endpoints on the circle.

Central Angle - an angle whose vertex is the center of the circle.

Parts of a Circle:

Congruent Circles have congruent radii.

Fact!

To learn how people really spend their time, a research firm studied the hour-by-hour activities of 3600 people. The participants were between 18 and 90 years old. Each participant was sent a 24-hour recording sheet every March for three years from 2000 to 2002.

Example 1: Real – World Connection.

The study found that people spend most of their time sleeping, working, and watching television. Some information from the study is shown in this circle graph. Find the measure of each central angle in the circle graph.

An arc consists of 2 points on a circle and all the points in between them.

What is an arc?

Semicircle – an arc that covers half the circle.

Major Arc – an arc that is larger than a semicircle.

Minor Arc – an arc that is smaller than a semicircle.

Types of Arcs:

The measure of an arc is equal to the measure of its corresponding central angle, the central angle that intersects the arcs endpoints.

What is the measure of an arc?

Types of Arcs continued:

Id. the following arcs in circle O.◦ The minor arcs.

◦ The semicircles.

◦ The major arcs.

Example 2: Identifying Arcs

Adjacent arcs are arcs of the same circle that have exactly one point in common.

Fact!

The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Arc Addition Postulate

Homework: Pgs 389-390 #s 2 – 26 even.