1. 9-5 Tangents Objectives: To recognize tangents and use properties of tangents.

2. Vocabulary Tangent Point of Tangency Common Tangents Common External Tangents Common Internal Tangents Circumscribed Polygons

3. Definitions A line or line segment is tangent to a circle if it intersects the circle in exactly one point. The point of intersection between a tangent and its circle is called the point of tangency.

4. Theorem 9-8 If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

5. Example 1

6. Theorem 9-9 (Converse of Theorem 9-8) In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is tangent to the circle.

7. Example 2

8. Common Tangents A line or line segment that is tangent to two circles in the same plane is called a common tangent.

9. Common Tangents Common external tangents do not intersect the segment whose endpoints are the centers of the circles. Common internal tangents intersect the segment whose endpoints are the centers of the circles.

10. Theorem 9-10 If two segments from the same exterior point are tangent to a circle, then they are congruent.

11. Circumscribed Polygons A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle.

12. Example 3