Section 10 – 1

1. Section 10 – 1 Use Properties of Tangents

2. Vocabulary Circle – A set of all points that are equidistant from a given point called the center of the circle. Radius – A segment whose endpoints are the center and any point on the circle. Half the diameter. r = ½ d Diameter –A chord that contains the center of the circle. Twice the radius. d = 2r Chord – A segment whose endpoints are on a circle.

3. Secant –A line that intersects a circle in two points. Tangent –A line in the plane of a circle that intersects the circle in exactly one point. secant Point of tangency tangent B A

4. Theorem 10.1 In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. P Q m

5. Theorem 10.2 The Tangent segments from a common external point are congruent.

6. Example 1 Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. chord secant tangent

7. Example 2 Find the radius r of circle C. Use the Pythagorean Thm (r + 16)2 = r2 + 242 (r + 16)(r + 16) = r2 + 576 r2 + 16r + 16r + 256 = r2 + 576 r2 + 32r + 256 = r2 + 576 32r + 256 = 576 32r = 320 r = 10

8. Example 3 In circle C, AD is tangent at D and AB is tangent at B. Find x. Use Theorem 10-2 AB = AD 2x2 + 5 = 13 2x2 = 8 2 2 x2 = 4 x = 2

9. Homework Section 10-1 Page 655 – 658 1, 3 – 10, 12, 13, 21 – 26, 43 – 46