11-1 Tangent Lines

1
11-1Tangent Lines
Objective To use the relationship between a
radius and a tangent.
2
Vocabulary

• Tangent to a circle
• Point of tangency

• A line in the same plane of a circle that
  intersects the circle in exactly one point.
• The point where a circle and a tangent intersect.

3
Theorem 11-1

• If a line is tangent to a circle, then the line
  is perpendicular to the radius drawn to the point
  of tangency.

A
P
B
O
4
1 Finding Angle Measures

• is tangent to . Find the value of x.

D
E
xo
O
38o
5
2 Finding Angle Measures

• and are tangent to . Find the
  value of x.

L
M
x
117
O
Since and are tangent to
N
and are right angles.
LMNO is a quadrilateral whose angle measures have
a sum of 360.
6
Theorem 11-2

• If a line in the plane of a circle is
  perpendicular to a radius at its endpoint on the
  circle, then the line is tangent to the circle.

A
P
B
O
7
3 Finding a Tangent

• If NL 4, LM 7, and NM 8, is tangent to
  a at L?

M
8
7
L
4
N
8
4 Finding a Tangent

• If NL 7, LM 24, and NM 25, is tangent
  to a at L?

N
25
7
M
Yes
L
24
9
Assignment

• Page 586
• 1-3 10-12