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Session 25 Warm-up 1.Name a segment tangent to circle A. 2.What is the 3.If BD = 36, find BC. 4.If AC = 10 and BD = 24, find AB. 5.If AD = 7 and BD = 24, find BE. A D E C B

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Secant Angles and Secant – Tangent Angles

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A secant line intersects the circle at exactly two points.

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Case I: Vertex is ON the circle ANGLE ARC ANGLE ARC

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Ex. 1 Find m 1. A B C 124° 1 m 1 = 62

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Ex. 2 Find m 1. 84° 1 m 1 = 42

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Ex. 3 Find m 1. 108° 1 m 1 = 126

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Case II: Vertex is inside the circle A B C D ANGLE ARC

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Ex. 4 Find m 1. A B C D 1 93° 113° m 1 = 103

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Ex. 5 Find mQT. N Q T M 92 84 mQT = 100

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Case III: Vertex is outside the circle A B C D ANGLE LARGE ARC small ARC ANGLE LARGE ARC small ARC LARGE ARC ANGLE

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A B D 1 Ex. 6 Find m 1. 65° 15° m 1 = 25

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A B Ex. 7 Find mAB. 27° 70° mQT = 16

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1 Ex. 8 Find m 1. 260° m 1 = 80

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Lesson 9-6 Other Angles (page 357) Essential Question How can relationships in a circle allow you to solve problems involving angles of a circle?

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