9-5Tangents

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