Circles: Properties, Calculations, and Applications

Question 1

Calculate the circumference of a circle with a radius of 10 cm.

Accepted Answer

20π cm

Answer

10π cm

Answer

5π cm

Answer

2π cm

Question 2

Which of the following chords divides a circle into two equal arcs?

Accepted Answer

Diameter

Answer

Radius

Answer

Secant

Answer

Tangent

Question 3

Which of the following is a tangent to a circle?

Accepted Answer

Line touching the circle at one point

Answer

Line intersecting the circle at two points

Answer

Line passing through the center of the circle

Answer

Line parallel to the circle

Question 4

Determine the length of the arc intercepted by a central angle of 60° in a circle with a radius of 5 cm.

Accepted Answer

2.5π cm

Answer

5π cm

Answer

10π cm

Answer

12.5π cm

Question 5

Which of the following is a sector of a circle?

Accepted Answer

Region enclosed by two radii and an arc

Answer

Triangle formed by three radii

Answer

Quadrilateral formed by two chords and two radii

Answer

Polygon formed by multiple chords

Question 6

Which of the following describes a chord of a circle?

Accepted Answer

A line segment that intersects the circle at two distinct points

Answer

A line segment that passes through the center of the circle

Answer

A curved line that touches the circle at exactly one point

Answer

A closed figure that encloses the circle

Question 7

What is the equation of a circle with radius 'r' and center at (h, k)?

Accepted Answer

(x - h)^2 + (y - k)^2 = r^2

Answer

(x + h)^2 + (y + k)^2 = r^2

Answer

x^2 + y^2 = r

Answer

x^2 - y^2 = r

Question 8

If the length of a chord is 8 cm and the distance from the chord to the center of the circle is 6 cm, what is the radius of the circle?

Accepted Answer

12 cm

Answer

10 cm

Answer

14 cm

Answer

16 cm

Question 9

A circle has an area of 25π cm^2. What is its radius?

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 10

The formula for calculating the circumference of a circle is:

Accepted Answer

2πr

Answer

πr^2

Answer

4πr^2

Answer

πd

Question 11

What is the area of a circle with a radius of 7 cm?

Accepted Answer

49π cm^2

Answer

14π cm^2

Answer

7π cm^2

Answer

49 cm^2

Question 12

Which of the following equations represents a circle with center (2, 3) and radius 5?

Accepted Answer

(x - 2)^2 + (y - 3)^2 = 5

Answer

(x + 2)^2 + (y + 3)^2 = 25

Answer

2x + 3y = 5

Answer

x^2 + y^2 - 4x - 6y + 13 = 0

Question 13

A sector of a circle has an area of 20π cm^2 and a central angle of 120 degrees. What is the radius of the circle?

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 14

A circle has a circumference of 24π cm. What is the area of the circle?

Accepted Answer

36π cm^2

Answer

16π cm^2

Answer

64π cm^2

Answer

144π cm^2

Question 15

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

Accepted Answer

$(x - 2)^2 + (y + 3)^2 = 4$

Answer

$(x + 2)^2 + (y - 3)^2 = 4$

Answer

$(x - 2)^2 + (y - 3)^2 = 16$

Answer

$(x + 2)^2 + (y + 3)^2 = 16$

Question 16

What is the measure of the angle formed by two radii drawn to the endpoints of a diameter?

Accepted Answer

90 degrees

Answer

30 degrees

Answer

60 degrees

Answer

120 degrees

Question 17

Which of the following describes a tangent to a circle?

Accepted Answer

It is perpendicular to the radius at the point of contact.

Answer

It passes through the center of the circle.

Answer

It is parallel to the radius at the point of contact.

Answer

It intersects the circle at two points.

Question 18

What formula is used to calculate the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = dπ

Answer

C = πr²

Answer

C = 4πr

Question 19

A chord of a circle can be defined as:

Accepted Answer

A straight line intersecting the circle at exactly two distinct points.

Answer

A straight line intersecting the circle at its center.

Answer

A straight line with no points of intersection with the circle.

Answer

A straight line always perpendicular to a diameter.

Question 20

The formula for calculating the area of a circle with radius 'r' is:

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = 4πr

Answer

A = d²

Question 21

A tangent to a circle is characterized by:

Accepted Answer

Intersecting the circle at a single point.

Answer

Passing through the circle's center.

Answer

Being parallel to the radius.

Answer

Intersecting the circle at two distinct points.

Question 22

In a circle with a 10 cm radius, what is the length of a chord that lies 8 cm from its center?

Accepted Answer

6 cm

Answer

4 cm

Answer

8 cm

Answer

10 cm

Question 23

Which of the following defines a sector of a circle?

Accepted Answer

An area enclosed by two radii and part of the circumference.

Answer

An area enclosed by two chords and part of the circumference.

Answer

An area enclosed by a tangent and part of the circumference.

Answer

An area enclosed by a diameter and part of the circumference.

Question 24

What is the area of a sector in a circle with a 6 cm radius and a 60° central angle?

Accepted Answer

3π cm²

Answer

6π cm²

Answer

π cm²

Answer

0.5π cm²

Question 25

What is a primary property of a circle?

Accepted Answer

It has a constant radius from its center to any point on the circle.

Answer

It has only curved sides.

Answer

It is a regular shape.

Answer

It has only one diameter.

Question 26

Which formula calculates the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πd

Answer

C = πr^2

Answer

C = 4πr

Question 27

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

Accepted Answer

25π cm^2

Answer

50π cm^2

Answer

78.5 cm^2

Answer

100π cm^2

Question 28

What is a chord of a circle?

Accepted Answer

A straight line segment connecting two points on the circle.

Answer

A straight line segment passing through the center of the circle.

Answer

A straight line segment that touches the circle at only one point.

Answer

A straight line segment perpendicular to the circle.

Question 29

What is the length of the tangent drawn from a point outside a circle to the circle itself?

Accepted Answer

The perpendicular distance from the point to the center of the circle.

Answer

The distance from the point to the nearest point on the circle.

Answer

The distance from the point to the farthest point on the circle.

Answer

The radius of the circle.

Question 30

What is the measure of the arc intercepted by a central angle of 60 degrees?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

180 degrees

Answer

240 degrees

Question 31

Which is a theorem specifically related to circles?

Accepted Answer

Thales' Theorem

Answer

Pythagorean Theorem

Answer

Cosine Rule

Answer

Sine Rule

Question 32

What is the ratio of the circumference of a circle to its diameter?

Accepted Answer

π

Answer

1

Answer

2π

Answer

4π

Question 33

Which of the following lines touches a circle at exactly one point, called a point of tangency?

Accepted Answer

A tangent

Answer

A chord

Answer

A secant

Answer

A radius

Question 34

Which of the following is defined as a region bounded by two radii and the arc they intercept?

Accepted Answer

A sector

Answer

A segment

Answer

A chord

Answer

A diameter

Question 35

Which of the following is NOT a property of a cyclic quadrilateral?

Accepted Answer

All sides are congruent

Answer

Opposite angles add up to 180 degrees

Answer

All angles add up to 360 degrees

Answer

Diagonals bisect each other

Question 36

When a circle with a radius of 6 cm is cut in half, what is the area of the resulting semicircle?

Accepted Answer

18π cm²

Answer

12π cm²

Answer

24π cm²

Answer

36π cm²

Question 37

If the diameter of a circle is 10 cm, what is its radius?

Accepted Answer

5 cm

Answer

10 cm

Answer

15 cm

Answer

20 cm

Question 38

Which of the following is NOT a type of angle associated with circles?

Accepted Answer

Obtuse angle

Answer

Central angle

Answer

Inscribed angle

Answer

Reflex angle

Question 39

If a tangent is drawn to a circle from an external point P, and the length of the tangent is 10 cm and the radius of the circle is 5 cm, what is the distance from P to the center of the circle?

Accepted Answer

15 cm

Answer

5 cm

Answer

10 cm

Answer

20 cm

Question 40

Which of the following is a theorem related to circles?

Accepted Answer

Thales' Theorem

Answer

Pythagoras' Theorem

Answer

Cosine Rule

Answer

Sine Rule

Question 41

Which of the following accurately defines a chord of a circle?

Accepted Answer

A straight line intersecting the circle at two distinct points

Answer

A straight line touching the circle at only one point

Answer

A straight line passing through the center of the circle

Answer

A straight line parallel to the circle

Question 42

Determine the circumference of a semicircle with a radius of 10 cm.

Accepted Answer

20π cm

Answer

10π cm

Answer

30π cm

Answer

40π cm

Question 43

Which theorem is specifically related to circles?

Accepted Answer

Thales' Theorem

Answer

Pythagoras' Theorem

Answer

Angle Bisector Theorem

Answer

Midpoint Theorem

Question 44

What is the standard equation of a circle with radius 'r' and center (h, k)?

Accepted Answer

(x - h)² + (y - k)² = r²

Answer

x² + y² = r²

Answer

x² - y² = r²

Answer

(x + h)² + (y + k)² = r²

Question 45

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

Accepted Answer

25π square centimeters

Answer

10π square centimeters

Answer

50π square centimeters

Answer

100π square centimeters

Question 46

Find the circumference of a circle with a diameter of 10 centimeters.

Accepted Answer

10π centimeters

Answer

5π centimeters

Answer

15π centimeters

Answer

20π centimeters

Question 47

Which equation represents the circle passing through points (1, 2), (3, 4), and (5, 2)?

Accepted Answer

x² + y² - 10x + 16 = 0

Answer

x² + y² = 5

Answer

x² + y² - 10x - 16 = 0

Answer

x² + y² + 10x + 16 = 0

Question 48

Calculate the area of a sector of a circle with an angle of 60° and a radius of 10 centimeters.

Accepted Answer

20π square centimeters

Answer

10π square centimeters

Answer

30π square centimeters

Answer

40π square centimeters

Question 49

Which theorem is NOT related to circles?

Accepted Answer

Pythagoras' Theorem

Answer

Thales' Theorem

Answer

Angle Bisector Theorem

Answer

Inscribed Angle Theorem

Question 50

Which of the following is the equation of a circle with center (h, k) and radius r?

Accepted Answer

(x - h)^2 + (y - k)^2 = r^2

Answer

x^2 + y^2 = h^2 + k^2

Answer

x^2 - y^2 = r^2

Answer

(x + h)^2 + (y + k)^2 = r^2

Question 51

Calculate the area of a circle with radius 7 m.

Accepted Answer

49π m^2

Answer

7π m^2

Answer

14π m^2

Answer

98π m^2

Question 52

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

Accepted Answer

A line segment lying outside the circle

Answer

A line segment connecting two points on the circle

Answer

A line segment passing through the center of the circle

Answer

A line segment touching the circle at only one point