3. tangent
•A line that touches the
circle at only one point
secant
•A line that intersects the
circle at two points
Line 1
Line 2
A B
C
4. Postulate 2
•At any given point on a circle,
one and only one line can be
drawn that is tangent to the
given circle
Theorem 4.8
•If a line is perpendicular to a
radius at a point on the circle,
then the line is tangent to the
circle
A
B
N
5. Tangent segment
•A segment of a tangent line
Corollary 4.8.1
•Tangent segments formed
by tow tangent lines that
intersect at an external point
are congruent.
J
K
F
H
6. Corollary 4.8.2
•If two tangents of a circle
intersect at an external
point, then the line
segment from the center
of the circle to the
external point bisects the
angle formed by tangent
lines
J
K
F
H
7. Theorem 4.9
•If a line is tangent to a
circle, then it is
perpendicular to a
radius at a point on a
circle.
J
K
F
H
8. Theorem 4.10
•The measure of an angle formed by a chord and a
tangent intersecting at the point of tangency is half
the measure of the intercepted arc
Theorem 4.11
•The measure of an angle formed by two intersecting
chords in a circle is half the sum of the measure of
the intercepted arcs of the angle and its vertical
angles
9. Example 1
Given the figure, find x and y.
4x
y
2x
Solution:
1 rotation = 360
½ rotation = 180
2x + 4x = 360
6x = 360
x = 60
2x = 2(60)
= 120
y =
1
2
(2x)
=
1
2
120
= 60
