Pg 603. An angle whose vertex is the center of the circle.
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Transcript of Pg 603. An angle whose vertex is the center of the circle.
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