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

Unit Question: What happens when line segments intersect a circle? Today’s Question: How do you find the measure of angles formed by secant and tangent lines?

Secant Angles and Secant – Tangent Angles

measure of an arc = measure of central angle A B C Q 97  m AB m ACB m AE E = = = 97° 263° 83°

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

A secant line intersects the circle at exactly two points.

Ex. 1 Find m  1. A B C 124° 1 m<1 = 62 0

Ex. 2 Find m  1. 84° 1 m<1 = 42 0

Remember, a straight angle is 180 degrees!

Ex. 3 Find m  ° 1 m<1 = 126 0

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 0

Ex. 5 Find mQT. N Q T M mQT = 100 0

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 0

A B Ex. 7 Find mAB. 27° 70° m AB = 16 0

1 Ex. 8 Find m  ° m<1 = 60 0