1. 11-1 Tangent 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. P O A B

4. #1 Finding Angle Measures is tangent to. Find the value of x. D O xoxo E 38 o

5. #2 Finding Angle Measures 117° x°x° and are tangent to. Find the value of x. Since and are tangent to and are right angles. LMNO is a quadrilateral whose angle measures have a sum of 360°. L M N O

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. P O A B

7. #3 Finding a Tangent If NL = 4, LM = 7, and NM = 8, is tangent to a at L? N L M 4 7 8

8. #4 Finding a Tangent 7 24 25 N M L If NL = 7, LM = 24, and NM = 25, is tangent to a at L? Yes