Free Printable All About Circles

1.

What type of angle is

\angle

POR?

a)

inscribed

b)

central

c)

circumscribed

d)

tangent

2.

What type of angle is

\angle

PQR?

a)

central

b)

circumscribed

c)

inscribed

d)

tangent

3.

What is the measure of arc PR?

a)

90 degrees

b)

180 degrees

c)

45 degrees

d)

not enough information

4.

What is the measure of arc PQR?

a)

240 degrees

b)

270 degrees

c)

300 degrees

d)

not enough information

5.

What is the measure of

\angle

PQR?

a)

90 degrees

b)

180 degrees

c)

not enough information

d)

45 degrees

6.

Why do you know for certain that angle Y is a right angle?

a)

it is an inscribed angle

b)

the hypotenuse is a diameter

c)

it just looks right

d)

you can't know for certain

7.

Calculate the area of this sector. Use 3.14 for pi. Round to the tenths place.

a)

48 square units

b)

201.1 square units

c)

33.5 square units

d)

240.3 square units

8.

Betty wants to buy fence for the intercepted arc of the circle. The arc length is how much fence she needs to buy, so how much does she need? Use 3.14 for pi. Round to the nearest tenth.

a)

33.5 feet

b)

8.4 feet

c)

50.2 feet

d)

24.4 feet

9.

Calculate the area of this sector. Use 3.14 for pi. Round to the nearest tenth.

a)

42.7 sq cm

b)

87.2 sq cm

c)

24.2 sq cm

d)

10.4 sq cm

10.

Calculate the length of the red arc shown. Use 3.14 for pi. Round to the nearest tenth.

a)

30.5 cm

b)

24.4 cm

c)

12.2 cm

d)

8.72 cm

11.

In order to write the equation of any circle, what are the 2 essential facts you must know?

a)

the area (A) and the diameter (d)

b)

the center (h,k) and the radius (r)

c)

the diameter (d) and the radius (r)

d)

the circumference (C) and the radius (r)

12.

The circle has a center of (5,-9) and a radius of 12. What is the equation of this circle?

a)

$\left(x\ +\ 5\right)^2\ +\ \left(y-9\right)^2=144$

b)

$\left(x\ -\ 5\right)^2\ +\ \left(y\ -\ 9\right)^2\ =12$

c)

$\left(x\ +\ 5\right)^2\ +\ \left(y\ +\ 9\right)^2=\ 12$

d)

$\left(x\ -\ 5\right)^2\ +\ \left(y\ +\ 9\right)^2\ =144$

13.

The diameter AB is 10, and the center of the circle is (0,0). What is the equation of this circle?

a)

$x^2\ +y^2=100$

b)

$x^2+\left(y-10\right)^2=25$

c)

$x^2+y^2=25$

d)

$x^2+y^2\ =5^2$

14.

The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can be irrigated? Use 3.14 for pi. Round to the nearest tenth.

a)

401.9 sq m

b)

452.2 sq m

c)

256.3 sq m

d)

123.4 sq m

15.

What is the area of the sector occupied by flowers planted in the circle with a radius 4 m and a central angle of 45°? Use 3.14 for pi. Round to the nearest tenth.

a)

10.5 sq m

b)

12.4 sq m

c)

6.3 sq m

d)

18 sq m

16.

The ends of the diameter of a circle are the points A = (−5, 3) and B = (3, 1). What is the equation of this circle?

a)

$\left(x\ -\ 1\right)^2\ +\ \left(y\ +2\right)^2=\sqrt{68}$

b)

$\left(x\ +\ 1\right)^2+\ \left(y\ -\ 2\right)^2\ =\ 68$

c)

$x^2\ +\ y^2\ =\ 68$

d)

$x^2\ +\ \left(y\ -\ 2\right)^2\ =\ \sqrt{68}$

17.

A cell phone tower is designed to service a 12 mile radius. The tower is located at (3,-5) on a coordinate plane whose units represent miles. What is the equation of the outer boundary of the region serviced by the tower?

a)

$\left(x\ -\ 3\right)^2\ +\ \left(y\ +\ 5\right)^2=12$

b)

$\left(x\ +\ 3\right)^2+\left(y\ -\ 5\right)^2\ =12$

c)

$\left(x\ +\ 3\right)^2\ +\ \left(y\ -5\right)^2=144$

d)

$\left(x\ -\ 3\right)^2+\ \left(y\ +5\right)^2=144$

18.

A cell phone tower is designed to service a 12 mile radius. The tower is located at (3,-5) on a coordinate plane whose units represent miles. Will a cell phone user at (-7,4) have any service?

a)

yes

b)

no

19.

Write the equation of this circle. Use 3.14 for pi. Round to the nearest tenth.

a)

$\left(x\ -\ 3\right)^2\ +\ \left(x\ -1\right)^2\ =5$

b)

$x^2\ +\left(y\ -3\right)^2=25$

c)

$\left(x\ -\ 3\right)^2+\left(y\ -1\right)^2=25$

d)

$\left(x+3\right)^2+\left(y+1\right)^2=5$

20.

The given end points of the diameter are (−2,4) and (4,8). The center point of the circle is the center of the diameter, which is the midpoint between (−2,4) and (4,8). What are the coordinates of the center of the circle?

a)

(3,5)

b)

(0,6)

c)

(1,6)

d)

(2,4)

21.

The given end points of the diameter are (−2,4) and (4,8). The center point of the circle is the center of the diameter, which is the midpoint between (−2,4) and (4,8). What is the length of the radius of this circle? Round to the nearest tenth.

a)

7.2 units

b)

9.4 units

c)

5.3 units

d)

6.7 units

22.

Line segment EB is 24 units, line segment EP is 7 units. Calculate the length of line segment PB.

a)

25 units

b)

35 units

c)

22 units

d)

15 units

23.

How long is line segment OC?

a)

8 cm

b)

6 cm

c)

15 cm

d)

9 cm

All About Circles

Total questions: 23

Worksheet time: 48mins

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