Download Geometry: Angle Measures in Circles

II. P. Geometry Angle Measures in Circles
Angle Measures in Circles lesson 67
Line/Segment Position and Measure with Illustration
Central angle
x
P
Central angles
from lines
Vertex is moved off of
center but is still in
interior.
P
x
Angle equals arc
mP  x 
m P 
x
P
mP  x 
Angles equal
average of
intercepted
arcs
y
x
x y
2
Vertex is on circle
x
x
Neither ray tangent
One ray tangent
P
Angle is half of
intercepted arc.
P
m P 
1
x
2
m P 
1
x
2
Vertices are outside circle
x
P
y
P
y
x
y
x
P
m P 
Neither ray tangent
x y
2
m P 
One ray tangent
x y
2
Both rays tangent
Angle is one-half of difference of intercepted arcs.