Section 9-2 Tangents

Theorem 9-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Point of Tangency

Corollary Tangents to a circle from a common point are congruent A P B

Theorem 9-2 If a line in the plane of a circle is perpendicular to the radius at its outer endpoint, then the line is tangent to the circle.

Tangent line

When each side of a polygon is tangent to a circle, the polygon is said to be circumscribed about the circle and the circle is inscribed in the polygon.

Common tangent A line that is tangent to each of two coplanar circles

Common internal tangent Intersects the segment joining the centers A B

Common external tangent Does not intersect the segment joining the centers. A B

Tangent circles Coplanar circles that are tangent to the same line at the same point

Externally Tangent l A B

Internally Tangent l C D