11-1Tangent Lines

Objective: To use the relationship between a radius and a tangent.

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.

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.

P

O

A

B

OPAB

#1 Finding Angle Measures

is tangent to . Find the value of x.

D

O

xo

ED O

E

38o

90ODE

3890180x

128180x

52x

#2 Finding Angle Measures

117° x°

and are tangent to . Find the value of x.ML OMN

Since and are tangent to

ML MNO

L and are right angles.

N

LMNO is a quadrilateral whose angle measures have a sum of 360°.

3601179090 x360297 x

63x

L

M

N

O

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.

P

O

A

B. o tangent tis OAB

#3 Finding a Tangent

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

MLN

N L

M

4

78

222 874

644916

6465 NO

#4 Finding a Tangent

7

24

25

N

ML

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

MLN

222 25247 62557649

625625 Yes