11-1 Tangent Lines

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

2. 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. Vocabulary

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° O 117° 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 4 L 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