Warm-up A 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N M 50 C P 3. MCY = 270 Find BC. B 2. Find ACB 20 B A M 312 20 90.

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Presentation transcript:

Warm-up A 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N M 50 C P 3. MCY = 270 Find BC. B 2. Find ACB 20 B A M 312 20 90 B 24 C C Y

6.5 Other Angle Relationships – On, Inside, and Outside of the Circle

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

REMEMBER: Find m1. A B 1 124° C m1 = 62º

Ex. 1: Find m1. 1 78° m1 = 39º

108° Ex. 2: Find m1. 1 m1 = 126º

Case II: Vertex is inside the circle ARC B ANGLE D ARC C Looks like a PLUS sign!

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

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

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

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

Ex. 7 Find mAB. A 27° 70° B mAB = 16º

Ex. 8 Find m1. 260° 1 m1 = 80º

52.5º 4 Brain Buster 32º 2 3 105º 36.5º 1 105º 16º