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Transcript 
11.4 Inscribed Angles: angles whose vertex is ON the
circle and whose sides contain
chords of the circle.
A
B
C
intercepted arc: arc on the interior of an inscribed
angle
Thm: The measure of an inscribed angle is equal
to one-half the measure of the intercepted
arc.
Examples.
1. Find mADC
2. Find mAC
B
B
C
A
D
A
70
C
3. Find m B
B
A
4. Find m A and m B
80
C
196
A
B
Thm: If 2 inscribed angles intercept the same arc, then
angles are congruent.
5. Find m LJM.
K
J
o
3y
(5y - 7)
L
M
o
Thm:
1. If a right triangle is inscribed in a circle, then the
hypotenuse is a diameter of a circle.
diameter
2. If one side of an inscribed triangle is a diameter,
then the triangle is right and the angle opposite
the diameter is right.
Defn.
inscribed polygon: all vertices are on the circle
circumscribed circle: circle around a polygon
touching all vertices of polygon.
3. A quadrilateral can be inscribed in a circle if and only
if the opposite angles are supplementary.
Find x.
6.
7.
x
3x
y
80
85
Find the measure of each angle of the quadrilateral.
A
19y
M
10y
40x
22x
H
T
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