11-2 chords & arcs 11-3 inscribed angles. theorems
TRANSCRIPT
11-2 Chords & Arcs11-3 Inscribed Angles
Theorems
If <ACB <ECD then AB ED
If AB ED then AB ED
If AB ED then <ACB <ECD
C
D
B
E
A
Theorems
If chords are congruent, then they are equidistant from the center of the circle.
If FG HI then JK JL
L
K
J
F
G
H I
Theorems
If the diameter is perpendicular to a chord, then it bisects the chord and its arcs.
The perpendicular bisector of a chord contains the center of the circle.
If MO NP then NQ PQ
& NO PO
Q
M
ON
P
Examples
1)Find AB. 2) Find AB & AO.
46.8Y
O
BA
77
4
4Y
X
O
D
E
BA
C
Vocabulary & Theorems
Inscribed Angle – angle whose vertex is on the circle.
Two inscribed angles intercept the same arc then they are congruent.
m<ABC = 1/2 AC
100
A
B
C
<ABC <ADC
A
B
CD
Theorems
Opposite angles of a quadrilateral inscribed in a circle are
supplementary.
An angle inscribed in a semicircle is a right angle.
m<B + m<E = 180m<A + m<C = 180
A
B
C
E
A
B
C
Examples
1) Find the numbered angles.
2) Find x and y.
65
43
2
1
5080
F
I H
G
y
x
70
90
80
B
A
D
C