100 100100100100

200 200 200 200 200

300 300300300300

400 400400400400

500 500500500500

Inscribed Angles

Tangents &

Angles

Secants,Tangents,

&Angles

SegmentsIn Circles

EquationsOf Circles

Inscribed Angles - 100

Answer: 90°

AB is a diameter. Find m<BCA.

A

C

B

35°

Inscribed Angles - 200

Answer: 50°

Find m<CBD.

C

A

B

D

50°

Inscribed Angles - 300

P

A

D

C

B

If the measure of arc AC = 72°, find m<ABC.

Answer: 72/2 = 36°

72°

36°

Inscribed Angles - 400

Find the measure of arc BD.

P

A

D

C

B 55°

Answer: m<BCD = 35°, so arc BD = 70°70°

35°

90°

Inscribed Angles - 500

Find the measure of arc ABD.

P

A

D

C

B

36°

55°

Answer: mAC = 72° and mCD = 110°,So mABD = 360 – (110 + 72) = 178°

72°

110°

70°

108°

Tangents and Angles - 100

Answer: 52 + x2 = 132, so x = 12 = BA

Find BA.

AB

P

5 8

5

Tangents and Angles - 200

Answer: 4x + 18 = 7x, so x = 6

Find x.

A

B

.P C

4x + 18 7x

Tangents and Angles - 300

Answer: m<BPA = 48°, so mBC = 48°

Find the measure of arc BC.

D

A

B

P C 42° 48°

48°

Tangents and Angles - 400

Answer: 100°

Find the measure of arc UV.

R

S

T

U

V

W

X

Y

Z 40°

50° 50°

40°

Tangents and Angles - 500

Answer: For UW: 32 + x2 = 52, UW = 4 For XW: 62 + x2 = 102, WX = 8, so UT = 4 + 8 = 12

Find UT.

R

S

T

U

V

W

X

Y

Z

2 3

4

6

3

3

4

4

8

8

6

6

Secants, Tangents, Angles - 100

Answer: m<EBC = 240/2 = 120°

Find m<EBC.

. D

A C

E

B

240°

120°

Secants, Tangents, Angles - 200

Answer: m<3 = (60 + 160)/2 = 110°

Find m<3.

60° D C

A B

1 4 2

3 C

160°

60° 80°

Secants, Tangents, Angles - 300

Answer: m<WXY = (105 – 55)/2 = 25°

Find m<WXY.

W

X Y

Z

105°

55°

200°

Secants, Tangents, Angles - 400

Answer: m<LJK = (40 + 170)/2 = 105º

Find m<LJK

150º

H

I

L

K

J

N M

40º

110º 20º

40º

Secants, Tangents, Angles - 500

Answer: 4x + 6x + 11x - 5 + 20x + 10 + 150 = 360,so x = 5. Then mKN = 110 º and mIM = 20º,so m<H = (110 - 20)/2 = 45 º

Find m<H

H

I

L K

J

N M

(11x - 5)º

(20x + 10)º(4x)º

(6x)º

150º

110º

20º

Segments in Circles - 100

Answer: 6·3 = 9x, x = 2

Find x.

D C

A

B

C

6

39

x

Segments in Circles - 200

Answer: 62 = 4(4 + x), x = 5

Find x. R

S

T U

6

x4

Segments in Circles - 300

Answer: 4(4 + x) = 3(8), x = 2

P

Find x.

O

N M

L

5

3

4 x

Segments in Circles - 400

Answer: x·x = 16 ·4, x = 8

Find x.

C

A B

C

4

16

x

D

Segments in Circles - 500

Answer: x(x + x) = 5(19.6),2x2 = 98, so x = 7

Find x.

H

G F E

14.6 5

x x

I

Equations of Circles - 100

Answer: (4, -5)

What are the coordinates of the center of a circle with equation (x – 4)2 + (y + 5)2 = 16

Equations of Circles - 200

Answer: √34 = 5.8

What is the radius of a circle, as a decimal to the nearest tenth, with equation: (x – 4)2 + (y + 5)2 = 34.

Equations of Circles - 300

Answer: (x + 1)2 + (y + 2)2 = 9

Write the equation for circle K.

K

Equations of Circles - 400

Answer: (x – 1)2 + y2 = 25

Find the equation of circle P.

P

Equations of Circles - 500

Answer: The center of the circle is (1, 0) and the radius is 2. The easiest way to find the coordinates of a point on the circle would be to move 2 units above (1, 2), below (1, -2), left (-1, 0), or right (3, 0) of the center.

Name the coordinates of a point on the circle with equation (x – 1)2 + y2 = 4