Secants, Tangents, &
Angle Measures
Section 10-6
secant – a line that intersects a
circle in exactly 2 points.
A secant of a circle contains a
chord of the circle.
Theorem 10.13
If a secant and a tangent
intersect at the point of
tangency, then the measure of
each angle formed is one-half
the measure of its intercepted
arc.
60o
120o
Theorem 10.12
If 2 secants intersect in the
interior of a circle, then the
measure of an angle formed is
½ the sum of the measures of
the arcs intercepted by the angle
and its vertical angle.
o
60
o
50
o
40
40  60
o
2
o
 50
o
Theorem 10.14
If 2 secants, a secant and a
tangent, or 2 tangents intersect in
the exterior of a circle, then the
measure of the angle formed is ½
the positive difference of the
measures of the intercepted arc.
55o
140o
30o
140  30
o
2
o
 55
o
Joke Time
What is an insect that’s not
feeling well?
Secant (sick ant)
Who was a famous person that
was not very healthy?
“I sick” Newton