9 5 Tangents Objectives To recognize tangents and

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

Vocabulary • • • Tangent Point of Tangency Common Tangents Common External Tangents Common Internal Tangents Circumscribed Polygons

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.

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

Example 1

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.

Example 2

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

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.

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

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

Example 3