The document discusses three theorems relating to angles and arcs in circles: 1) The Intercepted Arc Theorem states that if a tangent and chord intersect at one point, the measure of each angle is equal to half the measure of the intercepted arc. 2) The Angles Inside Circle Theorem states that if two chords intersect inside a circle, the measure of each angle is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle. 3) The Angles Outside Circle Theorem states that if a tangent and secant intersect outside a circle, the measure of the angle formed is equal to half the difference of the measures of the intercepted arcs.

1. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015
B
E
L
L
W
O
R
K
38
3.
x = 5
y = 10
2.
Find the value of each variable.
44

2. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015
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
C
A
2 1
m<1= 1/2 mAB
m<2= 1/2 m BCA

3. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015
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
C
B
A
2
1
m<1 = 1/2 (mDC + mAB)
m<2 = 1/2 (mAD + mBC)

4. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015
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.
A
C
B
1
P
Q
R
2
W
X
Z
Y
3
tangent & secant tangent & tangent secant & secant
m<1 = 1/2 (mBC ­ mAC) m<2 = 1/2 (mPQR ­ mPR) m<3 = 1/2 (mXY ­ mWZ)

5. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015

6. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015

7. 10.5 Angle Relationships in Circles
HW pg. 683 #3­17, 25
March 16, 2015
HW pg. 683 #3­17 & 25