Circles: Properties, Formulas, and Applications

Question 1

Which property is NOT characteristic of a circle?

Accepted Answer

Variable circumference

Answer

Constant radius

Answer

Two perpendicular radii

Answer

Constant diameter

Question 2

Which equation accurately represents the circumference of a circle with radius 'r'?

Accepted Answer

C = 2πr

Answer

C = πr

Answer

C = πr^2

Answer

C = 2πr^2

Question 3

Calculate the area of a circle with a 5 cm radius.

Accepted Answer

25π cm^2

Answer

50π cm^2

Answer

10π cm^2

Answer

15π cm^2

Question 4

Which describes a secant line to a circle?

Accepted Answer

Intersects the circle at two distinct points

Answer

Intersects the circle at one point

Answer

Never intersects the circle

Answer

Passes through the center of the circle

Question 5

Identify a property of a circle inscribed within a square.

Accepted Answer

Radius equals half the square's side length

Answer

Diameter equals the square's side length

Answer

Circumference equals the square's perimeter

Answer

Area equals half the square's area

Question 6

Which theorem is not related to circles?

Accepted Answer

Pythagorean Theorem

Answer

Intercept Theorem

Answer

Tangent-Chord Theorem

Answer

Chord-Chord Theorem

Question 7

Which equation represents the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πd

Answer

C = πr²

Answer

C = 2πr²

Question 8

What is the relationship between the radius (r) and diameter (d) of a circle?

Accepted Answer

d = 2r

Answer

r = 2d

Answer

d = 3r

Answer

r = 3d

Question 9

Which equation calculates the area of a sector?

Accepted Answer

A = (θ/180)πr²

Answer

A = (θ/360)πr²

Answer

A = (θ/90)πr²

Answer

A = (θ/45)πr²

Question 10

What is the measure of a central angle that intercepts an arc of 120 degrees?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

90 degrees

Answer

180 degrees

Question 11

Which of the following is **not** a part of a circle?

Accepted Answer

Surface area

Answer

Radius

Answer

Diameter

Answer

Chord

Question 12

What is the formula for the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πd

Answer

C = πr²

Answer

C = 4πr

Question 13

What is the diameter of a circle with a radius of 5 centimeters (cm)?

Accepted Answer

10 cm

Answer

2.5 cm

Answer

5 cm

Answer

20 cm

Question 14

What is the area of a circle with a radius of 3 centimeters (cm)?

Accepted Answer

9π cm²

Answer

3π cm²

Answer

18π cm²

Answer

6π cm²

Question 15

What is the equation of a circle with center (2, 3) and radius 4?

Accepted Answer

(x - 2)² + (y - 3)² = 4

Answer

(x - 3)² + (y - 2)² = 4

Answer

(x + 2)² + (y + 3)² = 4

Answer

(x + 3)² + (y + 2)² = 4

Question 16

What is the measure of the central angle that intercepts an arc of length 10 cm on a circle with radius 5 cm?

Accepted Answer

60°

Answer

90°

Answer

120°

Answer

180°

Question 17

Which of the following is **not** a theorem related to circles?

Accepted Answer

Pythagorean Theorem

Answer

Inscribed Angle Theorem

Answer

Tangent-Chord Theorem

Answer

Alternate Segment Theorem

Question 18

What is the circumference of a circle with a radius of 5 cm? (Use π to represent the mathematical constant approximately equal to 3.14)

Accepted Answer

10π cm

Answer

10 cm

Answer

25π cm

Answer

25 cm

Question 19

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

Accepted Answer

The area of a circle is equal to the product of its radius and circumference.

Answer

All points on a circle are equidistant from the center.

Answer

A circle can be divided into equal-sized sectors.

Answer

A circle has two radii and one diameter.

Question 20

What is the relationship between the radius and diameter of a circle?

Accepted Answer

The diameter is twice the radius.

Answer

The radius is twice the diameter.

Answer

The radius and diameter are equal.

Answer

There is no relationship between the radius and diameter.

Question 21

What is the measure of the central angle that intercepts an arc of 120 degrees?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

240 degrees

Answer

360 degrees

Question 22

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 = 25

Answer

(x - 3)² + (y + 2)² = 25

Answer

(x + 3)² + (y - 2)² = 25

Question 23

What is the length of the arc of a circle with radius 12 cm and central angle of 45 degrees? (Use π to represent the mathematical constant approximately equal to 3.14)

Accepted Answer

6π cm

Answer

12π cm

Answer

24π cm

Answer

48π cm

Question 24

Identify the property of a circle that is incorrect:

Accepted Answer

It has four right angles

Answer

It is a closed curve

Answer

All points on the circle are equidistant from the center

Question 25

Determine the formula used to calculate the circumference of a circle:

Accepted Answer

2πr

Answer

πr²

Answer

4πr

Answer

πr

Question 26

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

Accepted Answer

25π cm²

Answer

5π cm²

Answer

10π cm²

Answer

50π cm²

Question 27

Determine the diameter of a circle with a circumference of 10π cm:

Accepted Answer

5 cm

Answer

10 cm

Answer

2.5 cm

Question 28

Identify the definition of a tangent to a circle:

Accepted Answer

A straight line that intersects the circle at exactly one point

Answer

A straight line that intersects the circle at two points

Answer

A straight line that passes through the center of the circle

Question 29

Identify the definition of a sector of a circle:

Accepted Answer

A region bounded by two radii and the intercepted arc

Answer

A region bounded by a diameter and the intercepted arc

Answer

A region bounded by a chord and two radii

Question 30

Identify the definition of a cyclic quadrilateral:

Accepted Answer

A quadrilateral whose vertices lie on a circle

Answer

A quadrilateral whose angles are all equal

Answer

A quadrilateral whose sides are all equal

Answer

A quadrilateral whose diagonals are perpendicular

Question 31

Which of the following statements is NOT a characteristic of a circle?

Accepted Answer

Every point on a circle is equidistant from a point outside the circle.

Answer

A circle has only one center point.

Answer

Every point on a circle is equidistant from the circle's center.

Question 32

Which chord of a circle is the longest?

Accepted Answer

A chord that passes through the center of the circle

Answer

A chord that is perpendicular to a radius

Answer

A chord that is parallel to a diameter

Question 33

Which of the following theorems is NOT related to circles?

Accepted Answer

The Pythagorean Theorem

Answer

The Circle Tangent Theorem

Answer

The Inscribed Angle Theorem

Answer

The Angle Bisector Theorem

Question 34

The circumference of a circle is given by the formula:

Accepted Answer

2πr

Answer

4πr

Answer

πr

Answer

πr²

Question 35

The area of a circle is given by the formula:

Accepted Answer

πr²

Answer

2πr

Answer

4πr

Question 36

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

Accepted Answer

10π cm

Answer

5π cm

Answer

2π cm

Answer

25π cm

Question 37

Which of the following is the definition of a chord of a circle?

Accepted Answer

A line segment joining two points on a circle.

Answer

A line segment that is perpendicular to a radius of a circle.

Answer

A line segment that is parallel to a diameter of a circle.

Answer

A line segment that passes through the center of a circle.

Question 38

Which of the following is the definition of a sector of a circle?

Accepted Answer

A part of a circle bounded by two radii and an arc.

Answer

A part of a circle that is always equal to 180 degrees.

Answer

A part of a circle that is always greater than 180 degrees.

Answer

A part of a circle that is always less than 180 degrees.

Question 39

Which of the following is the definition of a segment of a circle?

Accepted Answer

A part of a circle bounded by a chord and two radii.

Answer

A part of a circle that is always less than 180 degrees.

Answer

A part of a circle that is always greater than 180 degrees.

Answer

A part of a circle that is always equal to 180 degrees.

Question 40

What is the circumference of a circle with a radius of 5 centimeters? (Use  π ≈ 3.14)

Accepted Answer

31.4 cm

Answer

15.7 cm

Answer

78.5 cm

Answer

25 cm

Question 41

A circle has a diameter of 12 inches. What is its area? (Use π ≈ 3.14)

Accepted Answer

113.04 sq. inches

Answer

37.68 sq. inches

Answer

36 sq. inches

Answer

452.16 sq. inches

Question 42

A pizza has a diameter of 10 inches. If the pizza is cut into 8 equal slices, what is the area of one slice? (Use π ≈ 3.14)

Accepted Answer

9.81 sq. inches

Answer

39.27 sq. inches

Answer

12.57 sq. inches

Answer

78.54 sq. inches

Question 43

A circular table has a circumference of 18.85 feet. What is the diameter of the table? (Use π ≈ 3.14)

Accepted Answer

6 feet

Answer

3 feet

Answer

9.425 feet

Answer

12 feet

Question 44

A circular pool has a radius of 4 meters. What is the area of the pool? (Use π ≈ 3.14)

Accepted Answer

50.24 sq. meters

Answer

12.56 sq. meters

Answer

25.12 sq. meters

Answer

100.48 sq. meters

Question 45

What is the name of the line segment that connects the center of a circle to a point on the circle?

Accepted Answer

Radius

Answer

Diameter

Answer

Chord

Answer

Arc