1. 10.5 Inside & Outside Angles February 20, 2013
Find the value of each variable. B
E
38 L
L
2. W
O
R
3. K
44
x=5
y = 10
Feb 21­1:31 PM
HW pg. 683 #3­17 & 25 1

2. 10.5 Inside & Outside Angles February 20, 2013
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 Inside & Outside Angles February 20, 2013
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 Inside & Outside Angles February 20, 2013
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
B X
P
A W
Q
1 3
2 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 Inside & Outside Angles February 20, 2013
Feb 21­4:04 PM
HW pg. 683 #3­17 & 25 5

6. 10.5 Inside & Outside Angles February 20, 2013
HW pg. 683 #3­17 & 25
Feb 21­4:04 PM
HW pg. 683 #3­17 & 25 6