Warm-up

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# Warm-up - PowerPoint PPT Presentation

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. The Circle. ( page 67) MM2G3 Students will understand the properties of circles .

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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

The Circle
• (page 67) MM2G3 Students will understand the properties of circles.
• (page 69) MM2G3bUnderstand and use properties of central, inscribed, and related angles .

Central Angle

Vertex OUTSIDE circle

Vertex ON circle

Vertex INSIDE circle

Ex. 1 Find m1.

A

B

1

124°

C

m1 = 62º

Ex. 2 Find m1.

1

84°

m1 = 42º

108°

Ex. 3 Find m1.

1

252°

m1 = 126º

Case II:Vertex is inside the circle

A

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.

mQT = 100º

N

Q

84º

92º

M

T

Central angle = ARC

Case III:Vertex 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.

1

15°

A

D

65°

B

m1 = 25º

Ex. 7 Find mAB.

mAB = 16º

A

27°

70°

B

Ex. 8 Find m1.

260°

1

100°

m1 = 80º

52.5º

4

32º

2

Brain Buster

3

105º

36.5º

1

105º

16º