Warm-up 1 st Hour - Geometry Unit 8 Test Scores: 105, 104, 100, 98, 96, 94, 94, 90, 86, 86, 84, 78, 75, 73, 73, 65, 61, 61, 60, 60, 47, 41, 37, 16, 16 Find : Mean=_____Median=_____ Mode=_____Range=_____

Warm-up 3 rd Hour - Geometry Unit 8 Test Scores: 105, 102, 101, 100, 98, 92, 92, 92, 86, 84, 82, 76, 76, 75, 73, 73, 73, 73, 70, 63, 61, 57, 57, 55, 50, 43 Find: Mean=_____Median=_____ Mode=_____Range=_____

Warm-up 6 th Hour - Geometry Unit 8 Test Scores: 104, 102, 98, 94, 92, 86, 86, 84, 82, 78, 76, 76, 76, 76, 75, 75, 73, 67, 67, 65, 63, 61 Find: Mean=_____Median=_____ Mode=_____Range=_____

Warm-up 7 th Hour - Geometry Unit 8 Test Scores: 106, 101, 100, 100, 100, 94, 90, 90, 90, 88, 84, 82, 82, 80, 78, 78, 76, 67, 60 Find: Mean=_____Median=_____ Mode=_____Range=_____

Section 10 – 1 Use Properties of Tangents

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. Chord – A segment whose endpoints are on a circle. center chord radius diameter

Diameter – A chord that contains the center of the circle. 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

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

Theorem 10.2 The Tangent segments from a common external point are congruent. R P T S

Example 1 Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. a. DC b. BD c. DE d. AE radius tangent diameter chord C D F B A E

Example 2 In the diagram, S is a point of tangency. Find the radius r of circle T. Use the Pythagorean Thm RT 2 = ST 2 + RS 2 (r + 36) 2 = r (r + 36)(r + 36) = r r r = r r = 2304 T r 36 cm RS r 48 cm 72r = 1008 r = 14 cm

Example 3 In circle C, DA is tangent at A and DB is tangent at B. Find x. Use Theorem 10-2 DA = DB 6x – 8 = 25 6x = C 25 B A 6x – 8 x = 5.5 D

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