Inscribed

1
Inscribed Angles
2
An angle ?ABC is an inscribed angle of a circle
if AB and BC are chords of the circle
A
C
B
3
The arc that lies in the interior of an inscribed
angle is the intercepted arc of the angle
A
C
B
4
Theorem 10.9 If an angle is inscribed in a
circle, then its measure is half the measure of
its intercepted arc
A
C
(
m?ABC ½ mAC
B
5
Theorem 10.9 Example
140?
A
C
70?
B
6
Theorem 10.10 If two inscribed angles of a
circle intercept the same arc, then the angles
are congruent
A
C
P
B
7
Theorem 10.10 If two inscribed angles of a
circle intercept the same arc, then the angles
are congruent
A
C
P
B
8
Theorem 10.11 An angle that is inscribed in a
circle is a right angle if and only if its
corresponding arc is a semicircle
C
A
B
180?
9
Theorem 10.12 A quadrilateral can be inscribed
in a circle if and only if its opposite angles
are supplementary
(
(
mDAB mDCB 360?
B
(
m?DCB ½ mDAB


(
A
m?DAB ½ mDCB
C
D
(
(
m?DCB m?DAB ½ mDAB ½ mDCB
(
(
½ (mDAB mDCB)
½(360?)
180?