Free Printable Chord Bisector Theorem

1.

If $\overline{BD}\cong\overline{DC}$ and $\overline{EF}\ \perp\ \overline{BC}$ , what conclusions can say about $\overline{EF}$ ?
(Hint: Use Chord Theorem #2)

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

2.

True or False?
If $\overline{EF}$ is a diameter to Circle A, then $\overline{BD}\cong\ \overline{DC}$ , $\overline{EF}\ \perp\ \overline{BC}$ , $measure\ of\ arc\ BE\cong\ measure\ of\ arc\ CE.$
(Hint: Use Chord Theorem #3)

a)

True

b)

False

3.

Determine the value of x and y.

a)

$x=64^{\circ\ }$ and $y=4$

b)

$x=4$ and $y=64^{\circ}$

c)

$x=116^{\circ}$ and $y=4$

d)

$296^{\circ}$ and $y=4$

4.

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.

5.

Determine if the following expression $3x-4=5x-18$ is true or false. Why?

a)

The expression $3x-4=5x-18$ is true because if a diameter is perpendicular to a chord, it is the bisector of the chord and its arcs.

b)

The expression $3x-4=5x-18$ is true because if a radius is perpendicular to a chord, it is the bisector of the chord and its arcs.

c)

The expression $3x-4=5x-18$ is false because if a diameter is perpendicular to a chord, it is the bisector of the chord only.

d)

The expression $3x-4=5x-18$ is false because if a diameter is perpendicular to a tangent line, it is the bisector of the diameter.

6.

$BD=12$ and $AC=3$ in circle A. Find the radius $AB.$

a)

$\sqrt{27}$

b)

$3\sqrt{5}$

c)

$6$

d)

$\sqrt{18}$

7.

Use the diagram of Circle A for the following question.
If $\overline{BE}\cong\overline{CD}$ , then what can you determine about the arc measures?
(Hint: Use Chord Theorem #1)

a)

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

b)

$measure\ of\ arc\ BE\cong measure\ of\ arc\ CD$

c)

$measure\ of\ arc\ BC\cong measure\ of\ arc\ ED$

d)

Not enough information

8.

Use Circle A for the following problem.
If measure arc BD is $125^{\circ}$ , then what is the measure of arc CD?
(Hint: Use Chord Theorem #1)

a)

$360^{\circ}$

b)

$140^{\circ}$

c)

$235^{\circ}$

d)

$250^{\circ}$

9.

Use circle A to answer the following questions.

If measure of arc BC is $80^{\circ}$ . Find the measure of arc CD.
Hint: Use the Chord Theorem #1)

a)

$140^{\circ}$

b)

$280^{\circ}$

c)

$80^{\circ}$

d)

$250^{\circ}$

10.

Use circle A to answer the following questions.

If measure of arc BC is $80^{\circ}$ . Find the measure of arc CD.
Hint: Use the Chord Theorem #1)

a)

$140^{\circ}$

b)

$280^{\circ}$

c)

$80^{\circ}$

d)

$250^{\circ}$

11.

Find the measure of Arc MN

a)

66

b)

73.5

c)

147

d)

33

12.

Find the measure of Arc MN

a)

96

b)

114

c)

228

d)

48

13.

Find the value of x.

a)

25

b)

30.25

c)

7

d)

38

14.

Find the value of x.

a)

25

b)

30.25

c)

7

d)

38

15.

Find the value of x.

a)

31,3

b)

8

c)

16.3

d)

-8

16.

Find the value of x.

a)

10

b)

181

c)

34

d)

40

17.

Find the value of x.

a)

15

b)

13

c)

3

d)

6

18.

Find the value of x.

a)

10

b)

181

c)

34

d)

40

19.

Find the value of x.

a)

12.5

b)

8

c)

35

d)

16

20.

Find the value of x.

a)

12.5

b)

8

c)

35

d)

16

21.

Find the measure of arc AB.

a)

17

b)

34

c)

68

d)

146

22.

What do we call the red line?

a)

Chord

b)

Arc

c)

Diameter

d)

Segment

Chord Bisector Theorem

Total questions: 22

Worksheet time: 2hrs 46mins

Similar Resources on Wayground