Circles: Interactive Quizzes and Practice Questions

Question 1

Which of the following is not a property of a circle?

Accepted Answer

Infinite number of circumferences

Answer

Equal radii

Answer

Single center point

Answer

Constant circumference-to-diameter ratio

Question 2

Which of the following is a theorem related to circles?

Accepted Answer

Circle Tangent Theorem

Answer

Pythagorean Theorem

Answer

Triangle Angle Sum Theorem

Answer

Parallel Lines Theorem

Question 3

Which equation represents the area of a circle?

Accepted Answer

A = πr²

Answer

C = πd

Answer

C = 2πr

Answer

d = 2r

Question 4

Calculate the area of a sector of a circle with a central angle of 60 degrees and a radius of 5 centimeters.

Accepted Answer

2.5π square centimeters

Answer

5π square centimeters

Answer

10π square centimeters

Answer

15π square centimeters

Question 5

A circle is inscribed in a square with a side length of 10 centimeters. Find the area of the circle.

Accepted Answer

25π square centimeters

Answer

50π square centimeters

Answer

100π square centimeters

Answer

200π square centimeters

Question 6

What is the area of a circle with circumference 20π cm?

Accepted Answer

50π cm²

Answer

25π cm²

Answer

100π cm²

Answer

200π cm²

Question 7

Which of the following is equivalent to the circumference of a circle with radius r?

Accepted Answer

2πr

Answer

πr²

Answer

4πr

Answer

πd

Question 8

Which of the following equations represents a circle with center at (2,3) and radius 4?

Accepted Answer

(x - 2)² + (y - 3)² = 16

Answer

(x + 2)² + (y + 3)² = 16

Answer

x² + y² - 2x - 3y = 16

Answer

x + y = 4

Question 9

Find the formula to calculate the area of a circle with radius r.

Accepted Answer

A = πr^2

Answer

A = πr

Answer

A = 2πr

Answer

A = 4πr^2

Question 10

Which of the following is NOT a property of circles?

Accepted Answer

Equal perimeters

Answer

Equal radii

Answer

Equal diameters

Answer

Equal areas

Question 11

A circle has a circumference of 20π cm. What is its radius?

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 12

What is the length of a chord that passes through the center of a circle called?

Accepted Answer

Diameter

Answer

Radius

Answer

Circumference

Answer

Area

Question 13

Determine the area of a circle with a radius of 5 cm:

Accepted Answer

25π cm²

Answer

10π cm²

Answer

50π cm²

Answer

100π cm²

Question 14

The radius of a circle is related to its diameter by:

Accepted Answer

Diameter is twice the length of the radius.

Answer

Radius is half the length of the diameter.

Answer

Radius and diameter are equal in length.

Answer

There is no fixed relationship between radius and diameter.

Question 15

Identify the statement that does NOT define a tangent line to a circle:

Accepted Answer

Intersects the circle at two points.

Answer

Intersects the circle at a single point.

Answer

Touches the circle at one point without intersecting it.

Answer

Passes through the circle's center.

Question 16

Given a circle with center (4, -2) and radius 7, write its equation:

Accepted Answer

(x - 4)² + (y + 2)² = 49

Answer

(x + 4)² + (y - 2)² = 49

Answer

(x - 2)² + (y + 4)² = 7

Answer

(x - 4)² + (y - 2)² = 7

Question 17

Which value cannot be a radius of a circle?

Accepted Answer

-3

Answer

0

Answer

π

Answer

2

Question 18

A circle has a radius of 5 centimeters. What is its circumference?

Accepted Answer

10π cm

Answer

25π cm²

Answer

10 cm

Question 19

Which of the following is the formula for the circumference of a circle?

Accepted Answer

C = 2π times radius

Answer

C = π times diameter

Answer

C = ½π times radius

Answer

C = ½π times diameter

Question 20

What is the area of a circle with a radius of 5 cm?

Accepted Answer

25π cm²

Answer

50π cm²

Answer

10π cm²

Answer

12.5π cm²

Question 21

What is the area of the circle with a diameter of 6 cm?

Accepted Answer

12π cm²

Answer

9π cm²

Answer

18π cm²

Answer

24π cm²

Question 22

Which of the following is a secant of a circle?

Accepted Answer

A line intersecting the circle at two points

Answer

A line touching the circle at one point

Answer

A line passing through the center of the circle

Answer

A line parallel to the circle

Question 23

What is the radius of a circle inscribed in a square with a side length of 8 cm?

Accepted Answer

4 cm

Answer

2 cm

Answer

6 cm

Answer

8 cm

Question 24

A circle with a circumference of 20π units has a diameter of:

Accepted Answer

10

Answer

15

Answer

5

Answer

20

Question 25

The area of a sector in a circle with a radius of 5 units and a central angle of 60 degrees is:

Accepted Answer

12.5π square units

Answer

100π square units

Answer

50π square units

Answer

25π square units

Question 26

The formula for calculating the circumference of a circle is:

Accepted Answer

2πr

Answer

2πd

Answer

πr

Answer

πd

Question 27

To find the area of a circle, which formula should you use?

Accepted Answer

πr²

Answer

πd²

Answer

2πr²

Answer

2πd²

Question 28

A circle has a circumference of 20π. What is its radius?

Accepted Answer

10

Answer

20

Answer

5

Answer

40

Question 29

If the radius of a circle is doubled, what effect will this have on the circumference?

Accepted Answer

The circumference will double

Answer

The circumference will remain the same

Answer

The circumference will triple

Answer

The circumference will quadruple

Question 30

If the diameter of a circle is halved, what effect will this have on the area?

Accepted Answer

The area will be halved

Answer

The area will quadruple

Answer

The area will double

Answer

The area will remain the same

Question 31

What is the equation of a circle with center (0, 0) and a radius of 5?

Accepted Answer

x² + y² = 25

Answer

x² + y² = 100

Answer

y² - x² = 25

Answer

x² - y² = 25

Question 32

Which of the following is a secant of a circle?

Accepted Answer

A line that intersects the circle at two points

Answer

A line that is parallel to the circle

Answer

A line that passes through the center of the circle

Answer

A line that touches the circle at one point

Question 33

What is the measure of the central angle that intercepts an arc of 60°?

Accepted Answer

60°

Answer

30°

Answer

120°

Answer

90°

Question 34

What is the formula used to calculate the circumference of a circle, where 'r' represents the radius?

Accepted Answer

2πr

Answer

πr²

Answer

4πr

Answer

πd

Question 35

Which formula correctly calculates the area of a circle, where 'r' represents the radius?

Accepted Answer

πr²

Answer

4πr²

Answer

2πr

Answer

πd²

Question 36

How is the circumference of a circle related to its diameter? (Use 'C' for circumference and 'd' for diameter)

Accepted Answer

C = πd

Answer

Diameter = πr

Answer

Area = πr²

Answer

Circumference = 2πr

Question 37

A semicircle has a diameter of 8 cm. What is its perimeter?

Accepted Answer

4π + 8 cm

Answer

16π cm

Answer

6π cm

Answer

24π cm

Question 38

A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?

Accepted Answer

25π cm²

Answer

100π cm²

Answer

50π cm²

Answer

12.5π cm²

Question 39

What is the formula for the circumference of a circle, where 'r' represents the radius?

Accepted Answer

2πr

Answer

πd

Answer

πr^2

Question 40

What is the formula for the area of a circle, where 'r' represents the radius?

Accepted Answer

πr^2

Answer

2πr

Answer

2πd

Answer

πd^2

Question 41

If the radius of a circle is 5 cm, what is its area?

Accepted Answer

25π cm^2

Answer

10π cm^2

Answer

5π cm^2

Answer

50π cm^2

Question 42

Which of these is NOT a characteristic of a circle?

Accepted Answer

Parallel sides

Answer

Chords that are the same length are equidistant from the center.

Answer

Inscribed angles subtend the same arc.

Answer

All points on the circle are the same distance from the center.

Question 43

What is a tangent line to a circle?

Accepted Answer

A line that touches the circle at exactly one point.

Answer

A line that is parallel to the circle.

Answer

A line that passes through the center of the circle.

Answer

A line that intersects the circle at two points.

Question 44

A circle has a radius of 5 cm. What is its circumference?

Accepted Answer

10π cm

Answer

15π cm

Answer

25π cm

Answer

5π cm

Question 45

What is the area of a circle with a radius of 10 cm?

Accepted Answer

100π cm²

Answer

50π cm²

Answer

200π cm²

Question 46

Which of the following is NOT true about circles?

Accepted Answer

Circles have only one axis of symmetry.

Answer

All points on the circle are equidistant from a single point inside the circle.

Answer

The diameter of a circle is twice the length of the radius.

Question 47

A sector of a circle has a central angle of 60 degrees. If the radius of the circle is 12 cm, what is the area of the sector?

Accepted Answer

144π/3 cm²

Answer

288π/3 cm²

Answer

216π/3 cm²

Answer

72π/3 cm²

Question 48

What is the diameter of a circle with a circumference of 36π cm?

Accepted Answer

36 cm

Answer

18 cm

Answer

72 cm

Answer

9 cm

Question 49

Which equation shows the relationship between the circumference (C) and radius (r) of a circle?

Accepted Answer

C = 2πr

Answer

C = πd

Answer

C = 4πr²

Answer

C = πr²

Question 50

A circle is inscribed in a square. The side length of the square is 10 cm. What is the area of the circle?

Accepted Answer

25π cm²

Answer

100π cm²

Answer

10π cm²

Answer

50π cm²

Question 51

What is the equation of a circle with center (2, 3) and radius 5?

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x - 2)² + (y + 3)² = 5

Answer

(x + 2)² + (y - 3)² = 25

Answer

(x + 2)² + (y + 3)² = 5

Question 52

A circle has a diameter of 14 cm. What is the length of a chord that is 6 cm from the center of the circle?

Accepted Answer

8 cm

Answer

4 cm

Answer

12 cm

Answer

10 cm

Question 53

What is the ratio of the areas of two circles whose radii are in a ratio of 2:3?

Accepted Answer

4:9

Answer

2:3

Answer

3:4

Answer

9:4