Secants, Tangents and Angle Measures

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Presentation transcript:

Secants, Tangents and Angle Measures Chapter 10-6

Find measures of angles formed by lines intersecting on or inside a circle. secant Find measures of angles formed by lines intersecting outside the circle. Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key) Standard 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. (Key) Lesson 6 MI/Vocab

Tangent-Chord (or secant) Theorem If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half its intercepted arc 100o X Y mX = ½ (100o) mX = 50o mY = ½ (260o) mY = 130o

Secant-Tangent Angle 110o Answer: 55 Lesson 6 Ex2

A. 122 B. 58 C. 106 D. 116 A B C D Lesson 6 CYP2

2-Chord (or Secant) Theorem If 2 chords intersect in the interior of a circle, then the measure of the angle formed is one half of the sum of the arcs intercepted by the angle and its vertical angle. 100o X 40o mX = ½ (100 + 40) mX = ½ (140) mX = 70o

Secant-Secant Angle Method 1 Lesson 6 Ex1

Secant-Secant Angle Method 2 Answer: 98 Lesson 6 Ex1

A. 42 B. 84 C. 96 D. 138 A B C D Lesson 6 CYP1

2-Line Theorem If 2 lines intersect on the exterior of a circle, then the measure of the angle formed is one half of the difference of the 2 intercepted arcs.

Example: 100o X 40o mX = ½ (100 - 40) mX = ½ (60) mX = 30o

Secant-Secant Angle Find x. Answer: 17 Lesson 6 Ex3

Find x. A. 76 B. 73 C. 111 D. 146 A B C D Lesson 6 CYP3

JEWELRY A jeweler wants to craft a pendant with the shape shown JEWELRY A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant. 360 – x Answer: 220 x Lesson 6 Ex4

PARKS Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of A. A. 75 B. 127.5 C. 105 D. 52.5 A B C D Lesson 6 CYP4

Secant-Tangent Angle Find x. 141° 62° x° 62 = (141 – x) 124 = 141 – x –17 = –x 17 = x Answer: x = 17 Lesson 6 Ex5

Find x. A. B. 5 C. 9 D. A B C D Lesson 6 CYP5

Homework Chapter 10.6 Pg 603 6 – 26, 32 – 34, 55 – 57