CIRCLE THEOREMS
RADIUS/TANGENT
If a radius intersects a tangent at its point of tangency, then the radius
is perpendicular to the tangent.
INSCRIBED ANGLE
If an angle is a secant-secant inscribed angle or a secant-tangent
inscribed angle, then its measure is ½ of the arc it intercepts.
A
E
1
mD= EFD
2
B
C
D
1
mC= AB
2
F
SECANT ANGLE (VERTEX IN CIRCLE)
If an angle is a secant angle with vertex inside of the circle, then it is
equal to the average of the arc it intercepts and the arc intercepted
by its vertical angle.
H
G

J
I
1
= (mGH+mJI)
2
SECANT ANGLE: VERTEX OUT OF CIRCLE
If an angle is a secant angle with vertex outside of the circle, then the
measure of the angle is equal to ½ the difference of the 2 arcs it
intercepts.
 This theorems holds if the angle is secant-tangent
1
= (mGH-mJI)
2
D
G
EF is tangent
H
1
= (mDF-mGF)
2
G
J

I
E

F
RADIUS AND CHORDS
If a radius bisects a chord than it is perpendicular to the chord
If a radius is perpendicular to a chord, then it bisects the chord.
INTERSECTING CHORDS
If two chords intersect in a circle, the product of the parts of each
chord are equal.
If chords AB and CD intersect at point E, then (AE)(EB)=(CE)(ED)
B
C
E
A
D
SECANT SEGMENTS OUTSIDE CIRCLE
If two secant segments share an endpoint and have other endpoints on
a circle, then the products of the secant segment and outer part of the
secant segment will be equal.
 Holds true for tangent-secant
H
C
(AB)(AC)=(AD)(AD)
(AB)(AC)=(AD)2
G
B
J
F
I
A
D
(FG)(FH)=(FI)(FJ)
AD is tangent
TANGENT TANGENT
If two tangent segments intersect outside of the circle at the same
point, then the tangent segments are equal.
A
(AB and BC are
tangents)
B
AB  BC
C
The angle formed by tangent-tangent is supplementary to the minor
arc it intercepts.
A
(AB and BC are
tangents)
B
C
mB+mAC=180