10-6 Circles and Arcs

Objectives

To find the measures of central angles and arcs

To find the circumference and arc length

Image Long Description

In a plane, a circle is the set of all points equidistant from a given point called the center. You name a circle by its center. Circle P ((P) is shown below.

A diameter is a segment that contains the center of a circle and has both endpoints on the circle. A radius is a segment that has one endpoint at the center and the other endpoint on the circle. Congruent circles have congruent radii. A central angle is an angle whose vertex is the center of the circle.

Essential Understanding You can find the length of part of a circle's circumference by relating it to an angle in the circle.

An arc is a part of a circle. One type of arc, a semicircle, is half of a circle. A minor arc is smaller than a semicircle. A major arc is larger than a semicircle. You name a minor arc by its endpoints and a major arc or a semicircle by its endpoints and another point on the arc.

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