Free Printable Tangents, Secants, Special Segments, & Equations of Circles

1.

Solve for x.

a)

16

b)

34

c)

10

d)

19

2.

Solve for x

a)

5

b)

9

c)

36

d)

8

3.

a)

15

b)

12

c)

5.5

d)

8.5

4.

Solve for x

a)

36

b)

60

c)

48

d)

24

5.

Solve for x

a)

4

b)

8

c)

6

d)

16

6.

It is the part of a secant segment that is outside a circle.

a)

Secant Segment

b)

Tangent Segment

c)

Outside Secant Segment

d)

External Secant Segment

7.

If a tangent and a secant are drawn from an to a circle, then the square of the length of the tangent is equal to the product of the length of the secant's external part and the length of the entire secant.

a)

internal point

b)

internal plane

c)

external point

d)

external plane

8.

AB and CD are chords of a circle (center O) that intersect at a point P inside the circle. Calculate the value of x.

a)

x = 4

b)

x = 6

c)

x = 8

d)

x= 9

9.

AB and CD are chords of a circle (center O) that intersect at a point P inside the circle. Calculate the value of y.

a)

y = 10.2

b)

y = 10.4

c)

y = 10.6

d)

y = 10.8

10.

Find the length of the unknown segment (x).

a)

x = 12

b)

x = 15

c)

x = 18

d)

x = 21

11.

Find the length of the unknown segment (x) in

a)

x = 6.11

b)

x = 6.24

c)

x = 6.32

d)

x = 6.57

12.

Find the length of the unknown segment (x)

a)

x = 6.64

b)

x = -6.64

c)

x = 12.64

d)

x = -12.64

13.

Find the length of the unknown segment (x)

a)

x = 4.8

b)

x = 5.0

c)

x = 6.3

d)

x = 7.2

14.

a)

12

b)

16

c)

18

d)

20

15.

Determine the external secant segment.

a)

$JO$

b)

$\overline{OS}$

c)

$\overline{SE}$

d)

$\overline{JO}$

16.

Solve for x.

a)

7.94

b)

8

c)

10.58

d)

112

17.

Find the value of y.

a)

2

b)

3

c)

9

d)

14

18.

Solve for x.

a)

10

b)

85

c)

170

d)

180

19.

Find the measure of angle ABD.

a)

14

b)

51

c)

37

d)

65

20.

a)

33

b)

18

c)

46

d)

16

21.

Find the measure of angle EFH.

a)

61

b)

65

c)

114

d)

130

22.

What is the value of JT that verifies segment JT is tangent to circle O if OT = 6in and JO = 10in?

a)

9.2 in

b)

8 in

c)

17.1 in

d)

11.7 in

23.

Determine the value of x in the diagram.

a)

14

b)

21

c)

22

d)

27

24.

Which equation correctly reflects the information shown in the diagram?

a)

(18)(14) = (3x)(3x + 6)

b)

(18)(3x) = (14)(3x + 6)

c)

(18)(3x + 6) = 14(3x)

d)

(18)+ (3x) = (14)+ (3x + 6)

25.

Solve for x in the diagram shown.

a)

x = 2

b)

x = 1

c)

x = 10

d)

x = 5

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

Tangent

b)

Secant

c)

Chord

d)

Radius

28.

a)

Tangent

b)

Secant

c)

Radius

d)

Chord

29.

a)

Chord

b)

Secant

c)

Radius

d)

Tangent

30.

a)

12

b)

7

c)

8

d)

4

31.

What is the measure of angle 2?

a)

80

b)

45

c)

125

d)

40

32.

Solve for x.

a)

29

b)

33

c)

41.5

d)

50

33.

Name a secant.

a)

BD

b)

DG

c)

HF

d)

AF

34.

What is the measure of angle HKI?

a)

72

b)

73

c)

74

d)

75

35.

Find the m∠MNQ.

a)

89⁰

b)

45⁰

c)

158⁰

d)

22⁰

36.

Find the m∠1.

a)

130⁰

b)

65⁰

c)

44⁰

d)

86⁰

37.

Find the measure of minor arc AV.

a)

55°

b)

115°

c)

85°

d)

95°

38.

What is the value of x?

a)

22

b)

25

c)

15

d)

20

39.

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

a)

54

b)

36

c)

48

d)

42

40.

Find the perimeter of the triangle.

a)

A

b)

B

c)

C

d)

D

41.

Find x. Assume that segments that appear to be tangent are tangent.

a)

2

b)

11

c)

7.6

d)

9

42.

Is line AB tangent to the circle?

a)

Yes

b)

No

43.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?"

a)

-15

b)

6

c)

15

d)

14

44.

Find x. Assume that segments that appear to be tangent are tangent.

a)

11.2

b)

18.0

c)

25.0

d)

30.0

45.

Lines AO and BO are tangent. What is the measure of BO?

a)

20

b)

15

c)

10

d)

5

46.

What is the correct way to write your equation?

a)

20 = y x 30

b)

$20^2\ =\ y\ x\ 30$

c)

$20^2=\ y\left(y\ x\ 30\right)$

d)

$20^2\ =y\left(30+y\right)$

47.

Find the perimeter of the polygon depicted.

a)

39.6

b)

33.8

c)

38

d)

43.5

48.

2. Line XD and ZD are tangents to circle A at points X and Z respectively. Major arc XCZ and minor arc XZ are the intercepted arcs of the angle created by the two tangents outside the circle. What relationship exists among the given figures?

a)

$m∠D=\frac{1}{2}m(arcXCZ-arcXZ)$

b)

$m∠D=\frac{1}{2}m(arcXCZ+arcXZ)$

c)

$m∠C=\frac{1}{2}m(arcXDZ-arcXZ)$

d)

$m∠C=\frac{1}{2}m(arcXDZ+arcXZ)$

49.

8. Line t is tangent to the circle. Find the indicated measure.

a)

a) $70\degree$

b)

b) $90\degree$

c)

c) $110\degree$

d)

d) $290\degree$

50.

9. Find the value of (6x-11)°.

a)

a) $16.5\degree$

b)

b) $55\degree$

c)

c) $110\degree$

d)

d) $235\degree$

51.

What can you conclude?

a)

AB and AC are not congruent.

b)

AB= half of AC

c)

AC = half of AB

d)

AB=AC

52.

In the figure,PA and PB are the tangents to a circle of centre 'O'. If ∠APB = 48⁰ then ∠AOP =

a)

68⁰

b)

66⁰

c)

56⁰

d)

76⁰

53.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

54.

What is the measure of arc YZX?

a)

231

b)

255

c)

168

d)

200

55.

If AB=8, AE=19, and CE=17, what is the measure of segment BC?

a)

6 units

b)

8 units

c)

8.5 units

d)

11 units

56.

Determine whether segment MP is tangent to the circle.

a)

YES

b)

NO

57.

What is the value of x if both segments are tangent to the circle?

a)

A

b)

B

c)

C

d)

D

58.

In the equation (x + 2)² + (y - 3)² = 4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

59.

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)

60.

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

a)

(x - 7)² + y² = 9

b)

(x + 7)² + y² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

61.

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

62.

What is the equation for this circle?

a)

(x+1)+(y+1)=9

b)

x²+y²=9

c)

x+y=9

63.

What are the coordinates of the center and the radius of the circle with an equation: (x + 7)² + (y - 6)² = 64 ?

a)

Center (7,-6)

Radius = 8 units

b)

Center (-7,6)

Radius = 64 units

c)

Center (-7,6)

Radius = 8 units

d)

Center (7,-6)

Radius = 64 units

64.

What is the center of the circle with equation x² + y² = 1?

a)

(1, 1)

b)

(0, 0)

c)

not enough information

65.

What is the equation of a circle whose diameter is 24 and whose center is at the origin?

a)

x²+y²=125

b)

x²+y²=64

c)

x²+y²=144

d)

x²+y²=576

66.

Write the equation of a circle with center (-5, 7) and a diameter 6 units.

a)

(x - 5)² + (y + 7)² = 36

b)

(x + 5)² + (y - 7)² = 36

c)

(x - 5)² + (y + 7)² = 9

d)

(x + 5)² + (y - 7)² = 9

67.

Which graph corresponds to

x²+ (y - 6)² = 9

a)

A

b)

B

c)

C

d)

D

68.

Which of the following shows a circle tangent to the y-axis? (Check all that apply.)

a)

b)

c)

d)

69.

Which of the following shows a circle tangent to the x-axis? (Check all that apply.)

a)

b)

c)

d)

70.

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

71.

Determine the equation of a circle with center (5,-3) and radius of 9

a)

x²+y²-10x+6y-47=4

b)

x²+y²-10x-6y-47=0

c)

2x²+y²+10x+6y-47=0

d)

x²+y²-10x+6y-47=0

72.

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

73.

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

74.

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

75.

Write the equation of the circle in general form.

a)

A

b)

B

c)

C

d)

D

76.

Convert the equation of the circle from standard to general.

a)

A

b)

B

c)

C

d)

D

77.

Write the equation of the circle in general form.

a)

A

b)

B

c)

C

d)

D

78.

Select the matching graph.

a)

b)

c)

d)

79.

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

a)

54

b)

36

c)

48

d)

42

80.

QS is a tangent to circle P. Find QS.

a)

144

b)

14

c)

12

d)

13

Tangents, Secants, Special Segments, & Equations of Circles

Total questions: 80

Worksheet time: 7hrs 4mins

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