9-5 tangents objectives: to recognize tangents and use properties of tangents
DESCRIPTION
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.TRANSCRIPT
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