Chapter 9 Circles 9 2 Tangents Objective I

Chapter 9 Circles 9 -2 Tangents Objective: I will be able to apply theorems that relate tangents and radii.

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. P O m

Corollary (p. 333) Tangents to a circle from a point are congruent. A 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. R Q l

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. B A C and D are internally tangent. D C

A B O P E C D Name a line that satisfies the given description. 1. Tangent to P but not to O. 2. Common external tangent to O and P. 3. 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: 1. PM 2. PR 3. NS 4. MQ 5. SR 6. NR

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