1. 10.5 Angle Relationships in Circles
March 05, 2014
Find the value of each variable.
38
2.
3.
B
E
L
L
W
O
R
K
44
x=5
y = 10
Feb 21­1:31 PM
HW pg. 683 #3­17, 25
1

2. 10.5 Angle Relationships in Circles
March 05, 2014
10.5 Angle Relationships in Circles
Intercepted Arc Theorem: If a tangent & chord intersect at 1 point,
then the measure of each angle = 1/2 measure of intercepted arc
B
m<1= 1/2 mAB
C
m<2= 1/2 m BCA
2 1
A
Feb 21­1:59 PM
HW pg. 683 #3­17, 25
2

3. 10.5 Angle Relationships in Circles
March 05, 2014
Intersecting Lines & Circles
on circle
inside circle
outside circle
Angles Inside Circle Theorem: if 2 chords intersect inside circle,
then the measure of each angle = 1/2 the sum of measures of the arcs
intercepted by the < and its vertical <.
D
m<1 = 1/2 (mDC + mAB)
A
1
2
C
m<2 = 1/2 (mAD + mBC)
B
Feb 21­3:16 PM
HW pg. 683 #3­17, 25
3

4. 10.5 Angle Relationships in Circles
March 05, 2014
Angles Outside Circle Theorem: if a tangent and secant intersect
outside a circle, then the measure of the angle formed = 1/2 the
difference of the measures of the intercepted arcs.
tangent & secant
tangent & tangent
secant & secant
X
B
P
A
Q
1
2
W
3
Z
Y
C
R
m<1 = 1/2 (mBC ­ mAC)
m<2 = 1/2 (mPQR ­ mPR)
m<3 = 1/2 (mXY ­ mWZ)
Feb 21­3:46 PM
HW pg. 683 #3­17, 25
4

5. 10.5 Angle Relationships in Circles
March 05, 2014
Feb 21­4:04 PM
HW pg. 683 #3­17, 25
5

6. 10.5 Angle Relationships in Circles
March 05, 2014
HW pg. 683 #3­17 & 25
Feb 21­4:04 PM
HW pg. 683 #3­17, 25
6