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CIRCLESUNIT PRACTICE PROBLEMS

Y

X

C

D

O

B

A

YX

C

D

O

B

A

C

O

A

B

1. OX OY .

OX = 15

5 5XB x

7 5CD x

a. Solve for x.

b. Find AB.

c. Find the length of the radius

2. 24AB CD .

The radius of circle O is 15.

2 7OX a .

a. Find OY.

b. Solve for a .

3. 8OA

100m AB

4 4m BOC x

a. Solve for x.

b. Find the length of AB

c. Find the area of sector AOB

CIRCLES UNIT PRACTICE PROBLEMS

O

A

B

C

D

C

OA

B

4. AB = 6

BC = 8.

a. Find the length of the radius

b. Find the area of the semicircle

5. The radius of a circle is 50. The distance from

the center of the circle to a chord on the circle

is 14.

a. Draw a diagram to represent this

information.

b. Find the length of the chord.

6. The length of a chord is 10. The distance from

the center of the circle to a chord on the circle

is 12.

a. Draw a diagram to represent this

information.

b. Find the length of the radius.

7. 80m B .

145m AD

58m AB

a. Find mCD .

b. Find m D .

c. Find mBC

CIRCLES UNIT PRACTICE PROBLEMS

8. The distance between the centers of two circles

is 39. The radius of one circle is 30. The

radius of the other circle is 15. The two circles

have a common external tangent.

Find the length of the common external tangent.

9. The radius of one circle is 12. The radius of

the other circle is 3. The length of their

common external tangent is 12.

Find the distance between the centers of the circles.

10. The distance between the centers of two circles

is 30. The radius of one circle is 9. The radius

of the other circle is 15. The two circles have a

common internal tangent.

Find the length of the common internal tangent.

CIRCLES UNIT PRACTICE PROBLEMS

K L

AW

O

N

E

C

S

T

N

E

C

S

T

11. WK = 11, WA = 9, and AL = 10. Find KL.

12. 20m SCT

23m ETN

a. Find mEN

b. Find mST

c. Find m TES

13. SE = 2

TN = 11

NC = 5

Find EC.

CIRCLES UNIT PRACTICE PROBLEMS

62

70

x

125

K

F

G

30

40

x

14. Solve for x :

15. Solve for x:

16. Find m K :

17. Find x :

40

62

143

164 112

x

210

x

x

CIRCLES UNIT PRACTICE PROBLEMS

BE

D

C

A F

BE

D

C

A F

18. Find x :

19. AB = 5

BC = 4

Find CD

20. ( 2)AE x

5EB

8ED x

2EF

a. Solve for x.

b. Find AB.

c. Find DF.

24

x

CIRCLES UNIT PRACTICE PROBLEMS

E

O

A

B

C

D

21. A circle with a radius of 13 is circumscribed

about a rectangle ABCD. AB = 24.

a. Draw the circle and rectangle.

b. Find BC.

22. 2AE x

2 1EB x

CE x

4ED x

a. Solve for x.

b. Find AB.

c. Find CD.

23. AB CD .

4 20m AB x

3 35mCD x

Find m AOB

C

D

O

A

B

CIRCLES UNIT PRACTICE PROBLEMS

24. FE = 6

CD = 9

BE = 4

a. Find A

B

b. Find D

E

DC

B

F

E

A

25. Given: C

Y

AN a. Solve for x

3 10AFN x b. Find measure of C

5 14C x c. What is the measure of arc AN

F

A

N

C

Y

CIRCLES UNIT PRACTICE PROBLEMS

26.

Given:

is isosceles, with base .

Circle , ,

ABC AC

P PQ AB PR CB

Prove: is isoceles.PQR

Statements Reasons

27.

Given: Circle O, XA YB

Prove: XAE YBE

Statements Reasons

A

C

B

Q

R

P

Y

A

B

E

X