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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.

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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



Case i vertex is on the circle
Case I: the CircleVertex is ON the circle

ANGLE

ARC

ARC

ANGLE


REMEMBER: Find the Circlem1.

A

B

1

124°

C

m1 = 62º


Ex. 1: Find the Circlem1.

1

78°

m1 = 39º


108 the Circle°

Ex. 2: Find m1.

1

m1 = 126º


Case II: the CircleVertex is inside the circle

A

ARC

B

ANGLE

D

ARC

C

Looks like a PLUS sign!


Ex. 4 Find the Circlem1.

93°

A

B

1

D

C

113°

m1 = 103º


Ex. 5 Find the CirclemQT.

mQT = 100º

N

Q

84º

92º

M

T


Case III: the CircleVertex is outside the circle

C

ANGLE

small ARC

A

D

LARGE ARC

B

LARGE ARC

LARGE ARC

small ARC

ANGLE

small ARC

ANGLE


Ex 6 find m 1
Ex. 6 Find the Circlem1.

1

15°

A

D

65°

B

m1 = 25º


Ex 7 find m ab
Ex. 7 Find the CirclemAB.

mAB = 16º

A

27°

70°

B


Ex 8 find m 1
Ex. 8 Find the Circlem1.

260°

1

m1 = 80º


52.5 the Circleº

4

32º

2

Brain Buster

3

105º

36.5º

1

105º

16º


Central Angle the Circle

Vertex OUTSIDE circle

Vertex ON circle

Vertex INSIDE circle


Homework: the Circle

Page 214 #s1-18


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