© Edgenuity, Inc.1

Lesson Goals

?

Lesson Question

Warm-Up

Central Angles

Apply

involving central angles, chords, arcs, tangents, and radii.

Identify

central angles, chords, and arcs.

Determine

of central angles, chords, and arcs.

Solve

problems using the radius-tangent theorem and its.

© Edgenuity, Inc.2

WK

2

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

Warm-Up

Central Angles

arc of a circlea part of a between two given endpointscentral anglean angle whose vertex is at the of a circle and whose sides are of that circlechorda segment with both on a circlepoint of tangencythe point of intersection between a circle and its radiusa that extends from the center of a circle to any point on the circletangenta line, line segment, or that intersects a circle at exactly one and contains no points inside the circle

© Edgenuity, Inc.3

Central Angles and Arc Measures

A

central angle

is an angle whose vertex is at the centerof a circle and whose sides are

radii

of that circle. •In circle

D

, segments

DF

, , and

DG

are all radii of the circle.The degree measure of an

arc of a circle

is equal to the degree measure of the central angle that intercepts it.•One central angle of circle

D

is

∠

. •It’s a central angle, because its vertex

D

is at the center, and sidesand

GD

are radii.•

EG °

Warm-Up

Central Angles

57

°

FGDEH

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