Free Printable Circles Review

1.

Assume that all the lines that appear tangent are tangent. Find the perimeter

a)

54

b)

36

c)

48

d)

42

2.

A point B is 17cm away from the centre O of a circle. AB is the tangent to the circle at A. Given that AB = 15 cm, find the radius of the circle.

a)

8 cm

b)

9 cm

c)

2 cm

d)

16 cm

3.

Find the length of LK

a)

24

b)

20.25

c)

17.5

d)

12.32

4.

Find the perimeter

a)

39.5

b)

32.8

c)

56.3

d)

79.2

5.

Which shows a tangent line?

a)

b)

c)

d)

6.

A tangent line intersects the circle ...

a)

in exactly two points

b)

in exactly one point

c)

through the center

d)

with the diameter

7.

Using the tangent lines, find the value of x.

a)

60

b)

120

c)

30

d)

300

8.

A tangent to a circle is ________________________ to the radius drawn to the point of tangency.

a)

congruent

b)

perpendicular

c)

complimentary

d)

supplementary

9.

Using lines tangent to the circle, find the value of x.

a)

57

b)

137

c)

47

d)

257

10.

QS is a tangent to circle P. Find QS.

a)

144

b)

14

c)

12

d)

13

11.

What is the measure of ∠PTQ?

a)

100°

b)

140°

c)

180°

d)

120°

12.

What is the measure of arc YZX?

a)

231

b)

255

c)

168

d)

200

13.

a)

A

b)

B

c)

C

d)

D

14.

What is m∠ACB?

a)

67.5°

b)

90°

c)

22.5°

d)

45°

15.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

16.

An angle in a circle with vertex on the circle itself

a)

Angle

b)

Central angle

c)

Inscribed angle

d)

Chord

17.

An angle in a circle with vertex on the center of the circle

a)

Central angle

b)

Angle

c)

Inscribed angle

d)

Circle

18.

What is the measure of arc AB?

a)

140

b)

142

c)

180

d)

153

19.

What is the value of x?

a)

x = 160

b)

x = 40

c)

x = 80

d)

x = 360

20.

a)

A

b)

B

c)

C

d)

D

21.

What best describes segment AB?

a)

chord

b)

secant

c)

tangent

d)

diameter

22.

Find the measure of arc JH

a)

93

b)

130

c)

120

d)

95

23.

The opposite angles of an inscribed quadrilateral are ____________________

a)

supplementary

b)

complementary

c)

vertical

d)

linear

24.

Quadrilateral ABCD is inscribed in the circle. Which sentence is true?

a)

A and B are supplementary

b)

A and C are supplementary

c)

m∠ A = m∠ B

d)

m∠ C = m∠ D

25.

$\angle K=$

a)

$45\degree$

b)

$135\degree$

c)

$88\degree$

d)

$8\degree$

26.

\angle X=

a)

$96\degree$

b)

$129$

c)

$84\degree$

d)

$49\degree$

27.

$\angle W=$

a)

$129\degree$

b)

$96\degree$

c)

$84\degree$

d)

$49\degree$

28.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

29.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

30.

Write the standard equation of the circle with the given center and radius; center (0,0) and radius: 3

a)

x²+y²=4

b)

x²+y²=81

c)

x²+y²=9

31.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

32.

What is the equation of the circle, with centre (-4,5) and radius 6 units?

a)

(x - 4)² + (y + 5)² = 6

b)

(x - 4)² + (y + 5)² = 36

c)

(x + 4)² + (y - 5)² = 6

d)

(x + 4)² + (y - 5)² = 36

33.

Is the point (3 , 5) inside, outside or on the circle with equation x² + y² = 9?

Hint, plug in the point to see if it makes a true statement (or graph on desmos.com)

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

34.

What is the equation of a circle with radius 4 and center (0, 8)?

a)

x² + (y-8)² = 16

b)

(x-8)² + y² = 4

c)

x² + (y-8)² = 4

d)

x² + (y+8)² = 16

35.

What is the radius of the circle with this equation of (x - 5)² + (y + 7)² = 8?

a)

4

b)

8

c)

4√2

d)

2√2

36.

Which graph corresponds to

(x+2)²+ (y-3)²=36

a)

A

b)

B

c)

C

d)

D

37.

Polygon MNQP is a square. If the radius of the circle is 5 cm, what is the length of QR?

a)

10 cm

b)

2.5 cm

c)

$5\sqrt{3}$

d)

$5\sqrt{5}$

38.

Line segments AB and CB are tangent to the circle. If the radius of the circle is 15 in and DB = 39 in, what is the value of AB?

a)

32

b)

36

c)

42

d)

25

39.

In the circle below point G is the center. The length of arc EF is

\frac{1}{6}

of the circumference of the circle. What is the value of

\angle EGF

?

(a)

40.

Find x.

a)

50

b)

25

c)

155

d)

310

41.

a)

110

b)

70

c)

55

d)

90

42.

Find AB.

a)

21

b)

42

c)

18

d)

58

43.

a)

180

b)

198

c)

252

d)

360

44.

a)

180

b)

76

c)

104

d)

142

45.

a)

37

b)

35

c)

24

d)

21.9

46.

a)

20

b)

11

c)

48

d)

4

47.

What is the standard equation of a circle?

a)

(x-k)² + (y-h)² = r²

b)

(x+h)² + (y+k)² = r²

c)

(x-h)² + (y-k)² = r²

d)

(k-x)² + (h-y)² = r²

48.

What does (h,k) standard for in the standard circle equation?

a)

(h,k) is the center of the circle

b)

(h,k) is a point on the circle.

c)

(h,k) is a point that we guess and find

d)

(h,k) is the distance of the circle

49.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

50.

What is the equation of a circle with radius 5 and center (-3, 4)?

a)

(x+3)² + (y-4)² = 5

b)

(x-3)² + (y-4)² = 25

c)

(x+3)² + (y-4)² = 25

d)

(x-3)² + (y+4)² = 5

51.

Choose the equation that represents the circle with center (5, 9) and goes through (2, 9)

a)

(x+5)²+(y+9)²=3

b)

(x-5)²+(y-9)²=3

c)

(x+5)²+(y+9)²=9

d)

(x-5)²+(y-9)²=9

52.

Find the equation of the circle with center (2,-3) and (6,−5) is on the circle?

a)

(x-2)²+(y+3)²=20

b)

(x+3)²+(y−8)²=-20

c)

(x-6)²+(y+5 )²=400

d)

(x-2)²+(y+3)²=164.

53.

$Write\ the\ center\ point\ of\ the\ circle\ \ x^2\ +\ y^2\ =\ 100$

a)

$\left(1\ ,\ 1\right)$

b)

$\left(-1,\ -1\right)$

c)

$\left(\ 10,\ 10\right)$

d)

$\left(\ 0,\ 0\right)$

54.

Write\ the\ center\ point\ of\ the\ circle\ \ \left(x-3\right)^2\ +\left(y\ +2\right)^2\ =36

a)

$\left(3,\ -2\right)$

b)

$\left(-3,\ 2\right)$

c)

$\left(2,3\right)$

d)

$\left(0,\ 0\right)$

55.

$Match\ the\ graph\ with\ it's\ equation$

a)

b)

c)

56.

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

a)

(x+2)² + (y+3)² = 49

b)

(x+2)² + (y+3)² = 13

c)

(x-2)² + (y-3)² = 49

d)

(x-2)² + (y-3)² = 13

57.

Determine the equation of the circle in standard form: x²+ y²+ 6x - 12y + 20 = 0

a)

(x-3)² + (y+6)² = 25

b)

(x+3)² + (y-6)² = 25

c)

(x-3)² + (y+6)² = 45

d)

(x+3)² + (y-6)² = 5

58.

Determine the center and radius:
x²+ y²- 10x + 8y -8 = 0

a)

C = (5,-4) r = 7

b)

C = (-5,4) r = 7

c)

C = (-4,5) r = 49

d)

C = (5,-4) r = 49

59.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

60.

Select the matching graph.

a)

b)

c)

d)

61.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

62.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

63.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

64.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

65.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

66.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

67.

In order to convert from general form to center-radius form, you must ___________.

a)

Multiply out

b)

expand

c)

complete the circle

d)

complete the square

68.

Find a and b.

a)

a=74 degrees
b=93 degrees

b)

a=93 degrees
b=74 degrees

c)

a=87 degrees
b=106 degrees

d)

a=106 degrees
b=87 degrees

69.

Find the value of x

a)

100

b)

105

c)

95

d)

90

70.

Find the value of d.

a)

115

b)

65

c)

96

d)

180

71.

What is the measure of angle A?

a)

34°

b)

180°

c)

101°

d)

79°

72.

Solve for x.

a)

14

b)

10

c)

11

d)

2

73.

Find a (Angle W)

a)

a=74 degrees

b)

a=93 degrees

c)

a=87 degrees

d)

a=106 degrees

Circles Review

Total questions: 73

Worksheet time: 6hrs 12mins

Similar Resources on Wayground