section 9-3 arcs and central angles. central angle an angle with its vertex at the center of a...

Section 9-3Arcs and

Central Angles

Central angle• An angle with its vertex at the center of a circle.

is a central angleABC

Circle B

ARC• an unbroken part of a circle

AC : read “arc AC”

Types of Arcs:1. Minor Arc: less than 180

• Measure is the same as its central angle• Named using two letters (Ex: )

2. Major Arc: more than 180• Measure is 360 minus the measure of its

central angle• Named using three letters (Ex: )

3. Semicircle: equals 180• Endpoints of a diameter • Named using three letters

PQR

AC

Adjacent Arcs

• Arcs in a circle that have exactly one point in common.

D

CB

A

m AB = 90andm BD = 30are adjacent arcs

Arc addition postulate

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

• Applies like segment addition postulate

D

CB

A

m = m PQRm AB = 90PQ + m m BD = 30QR = m ABD

Congruent Arcs• Arcs, in the same circle or in

congruent circles, that have equal measures.

Theorem 9-3• In the same circle or in

congruent circles, two minor arcs are congruent if and only if their central angles are congruent.