12.1 Tangent Lines • A

tangent to a circle

is a line in the plane of the circle that intersects the circle in exactly one point.

• The point where a circle and a tangent intersect is the

point of tangency

.

Theorem 12.1

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

Finding Angle Measures • Segment ML and segment MN are tangent to circle O. What is the value of x?

LMNO is a quadrilateral.

The sum of the angles is 360.

90 + 117 + 90 + x = 360 297 + x = 360 x = 63 The measure of angle M is 63 °.

Theorem 12.2

• 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.

Finding a Radius • What is the radius of circle C?

AB

2 

BC

2 

AC

2 12 2 

x

2  (

x

 8) 2 144 

x

2 16

x

 

x

2 80  16

x

 64

x

 5

Identifying a Tangent • Is segment ML tangent to circle N at L? Explain.

NL

2 

ML

2 

NM

2 7 2  24 2 625 ?

  25 2 625

Theorem 12.3

• If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.

More Practice!!!!!

• Homework – Textbook p. 767 # 6 – 17.