9-2 Tangents Theorem 9-1 (p. 333) If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. O P m

Corollary (p. 333) Tangents to a circle from a point are congruent. B P Given: and are tangent to the circle at A and B. By the corollary, ___ ___.

Theorem 9-2 p. 333 If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. Q R l

Circumscribed polygons 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. Circumscribed polygons Inscribed circles

A line that is tangent to each of two coplanar circles is called a common tangent. A common internal tangent intersects the segment joining the centers. A common external tangent does not intersect the segment joining the centers.

Tangent circles are coplanar circles that are tangent to the same line at the same point. A and B are externally tangent. C and D are internally tangent. A B C D

Name a line that satisfies the given description. B O P E D C Name a line that satisfies the given description. Tangent to P but not to O. Common external tangent to O and P. Common internal tangent to O and P. Answers:

P Q R M N S In the diagram, M and N are tangent to P. and are tangent to N. N has diameter 16, PQ = 3, and RQ = 12. Find the following lengths: PM PR NS MQ SR NR

Assignments CW: p. 335 1-5 ( before end of class) HW: p. 335 1-6, 10, 14, 16-18