Free Printable Arcs and Chord Properties

1.

Which segment is the diameter?

a)

AC

b)

BD

c)

LM

d)

CE

2.

Which segment is a radius?

a)

LM

b)

DC

c)

BD

d)

ML

3.

Which segment is a chord and NOT a diameter?

a)

LM

b)

DC

c)

AC

d)

BD

4.

Which of the following is a major arc?

a)

Arc AB

b)

Arc EDB

c)

Arc DLB

d)

Arc DMB

5.

Which of the following is a minor arc?

a)

Arc AB

b)

Arc EDB

c)

Arc DLM

d)

Arc DMA

6.

Which of the following is a semi-circle?

a)

Arc AB

b)

Arc EDB

c)

Arc DLB

d)

Arc DMA

7.

If $\overline{BE}\cong\overline{CD}$ , then what can you determine about the arc measures?
(Hint: Use Chord Theorem #3)

a)

$measure\ of\ arc\ BE\ +\ measure\ of\ arc\ CD=\ 360^{\circ}$

b)

$Arc\ BE\cong Arc\ CD$

c)

$Arc\ BC\cong Arc\ ED$

d)

Not enough information

8.

If measure arc BD is $140^{\circ}$ , then what is the measure of arc CD?
(Hint: Use Chord Theorem #3)

a)

$360^{\circ}$

b)

$140^{\circ}$

c)

$280^{\circ}$

d)

$80^{\circ}$

9.

If measure of arc BC is $80^{\circ}$ . Find the measure of arc CD.
Hint: Use the Chord Theorem #3)

a)

$140^{\circ}$

b)

$280^{\circ}$

c)

$80^{\circ}$

d)

$250^{\circ}$

10.

If $\overline{BD}\cong\overline{DC}$ and $\overline{EF}\ \perp\ \overline{BC}$ , what conclusions can say about $\overline{EF}$ ?
(Hint: Use Chord Theorem #1)

a)

$\overline{EF}$ is the radius of circle A

b)

$\overline{EF}$ is a secant line of circle A

c)

$\overline{EF}$ is the diameter of circle A

d)

$\overline{EF}$ is the tangent line of circle A

11.

Which of the following will make the statement true:
If $\overline{EF}$ is a diameter to Circle A and $\overline{EF}\ \perp\ \overline{BC}$ then
(Hint: Use Chord Theorem #2)

a)

$\overline{BD}\cong\overline{DC}$

b)

$ED=\frac{1}{2}BC$

c)

$Arc\ BC\ =\ \frac{1}{2}\ Arc\ BFC$

d)

$Arc\ BE\ =\ \frac{1}{2}\ Arc\ FC$

12.

$BD=8$ and $AC=3$ in circle A. Find the radius $AB.$

Hint: Use Chord Theorem #1 and the Pythagorean Theorem

a)

$4\sqrt{3}$

b)

$5$

c)

$4$

d)

$\sqrt{5}$

13.

Find the $measure\ of\ arc\ BD.$

Hint: Use Chord Theorem #4 and the sum of all the arcs in a circle is 360 degrees.

a)

$133^{\circ}$

b)

$266^{\circ}$

c)

$94^{\circ}$

d)

$188^{\circ}$

14.

Use the following diagram. What is the value of x and y?

Hint: This uses all the chord theorems and the Pythagorean Theorem

a)

$x=6\ and\ y=16$

b)

$x=16\ and\ y=6$

c)

$x=10\ and\ y=8$

d)

$x=8\ and\ y=10$

15.

Find the measure of Arc MN

a)

66

b)

73.5

c)

147

d)

33

16.

Use the diagram of circle A.

Which expression and deductive reasoning can be used to find the value of y?

a)

$2y+1=\ 5x-18$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chord is equal to its corresponding arc.

b)

$y+3=3x-4$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chord is equal to its corresponding arc.

c)

$y+4+2y+1$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chords are added together.

d)

$y+4=2y+1$ because if a diameter is perpendicular to a chord, its the perpendicular bisector to the chord. Therefore the chord is divided into two equal halves.

17.

Find the measure of arc JH if segments KH and JG are diameters.

a)

93

b)

130

c)

120

d)

95

18.

If the measure of arc ABC = 210°, what is the measure of ∠AOC?

a)

150°

b)

100°

c)

210°

d)

105°

19.

What is the measure of ∠PTQ?

a)

100°

b)

140°

c)

180°

d)

120°

20.

Find the arc measure for arc RQT

a)

335˚

b)

126˚

c)

224˚

d)

94˚

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

26.

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

27.

What is the center of the circle with this equation is (x+2)²+(y-4)²=41?

a)

(-2,41)

b)

(-2,4)

c)

(2,-4)

d)

(2,41)

28.

What is the radius of the circle

(x+7)²+(y-2)²=144?

a)

7

b)

12

c)

24

d)

144

29.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

30.

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

Arcs and Chord Properties

Total questions: 30

Worksheet time: 30mins

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