Secant Angles Secant-Secant Angles
Interior Secant Angle –
An angle formed when
two secants intersect
inside a circle.
Theorem 10.13
• A secant angle whose
vertex is inside a circle
is equal in measure to
half the sum of the
arcs intercepted by it
and its vertical angle.
mABE = 62.05 
m AE on
FC = 89.28 
mDBC = 62.05 
m DC on
FC = 34.82 
 
1
2
 m AE on
FC = 62.05 
FC+m DC on
E
A
B
C
D
Find
if
and
Secant-Secant Angles
Exterior Secant Angle – An
angle formed when two
secants intersect outside a
circle.
Theorem 10.14
• A secant angle whose
vertex is outside a circle is
equal in measure to half
the difference of its larger
and smaller intercepted
arcs.
mCBA = 25.41 
m ED on
FG = 21.03 
m CA on
FG = 71.84 
 
1
2
 m CA on
C
FG-m ED on
FG = 25.41 
E
B
D
A
Find x.
Tangent-Tangent Angles
Tangent-Tangent Angle –
An angle formed when
two tangents intersect in
the exterior of a circle.
Theorem 10.14
• A tangent-tangent angle
whose vertex is outside a
circle is equal in measure
to half the difference of its
larger and smaller
intercepted arcs.
B
E
A
C
D
PARKS Two sides of a fence to be built around a
circular garden in a park are shown. Use the figure
to determine the measure of