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

Secant Angles and Secant – Tangent Angles

A secant line intersects the circle at exactly two points.

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

Ex. 1 Find m  1. A B C 124° 1 m  1 = 62 

Ex. 2 Find m  1. 84° 1 m  1 = 42 

Ex. 3 Find m  ° 1 m  1 = 126 

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

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

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

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

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

A B Ex. 7 Find mAB. 27° 70° mQT = 16 

1 Ex. 8 Find m  ° m  1 = 80 