Arcs and ChordsPg 603

Central Angle

An angle whose vertex is the center of the circle

CentralAngle

A

B

C

Arcs

Minor Arc CB

Major Arc BDC

Semicircle Endpoints of the arc are a diameter

A

B

C

D

Measures of Arcs

Minor Arc The measure of the central angle

Major Arc 360 – minor arc

Congruent Arcs Have the same measure

360 - 56 = 304

56

56 A

B

C

D

Find the measures of the arcs

MN 80°

MPN 360 – 80 = 280°

PMN 180°

80R

N

P

M

Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. mABC = mAB +mBC

R

A

B

C

Find the measure of each arc.

GE 40 + 80 = 120°

GEF 120 + 110 = 230°

GF 360 – 230 = 130°

110

80

40

R

G

E

H

F

Theorem 10.4

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. if and only if

BCAB BCAB A

C

B

Theorem 10.5

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

GFDG EFDE

E

GD

F

Theorem 10.6

If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

J

KL

M

Find x.

40

402

x

xx(x+40)

2x

B

D

A

C

Find x.

x

7

Theorem 10.7

In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

EA

C

B

D

G

F

Find AB

CD = 10

EA

C

B

D

G

F