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Section 10 – 1 Use Properties of Tangents

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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.

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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. tangent secant Point of tangency BA

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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

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

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

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Example 2 Find the radius r of circle C. Use the Pythagorean Thm (r + 16) 2 = r 2 + 24 2 (r + 16)(r + 16) = r 2 + 576 r 2 + 32r + 256 = r 2 + 576 32r + 256 = 576 32r = 320 r = 10 r 2 + 16r + 16r + 256 = r 2 + 576

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

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

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