Circles: Master the Fundamentals of Geometry

Question 1

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

Accepted Answer

10π cm

Answer

10 cm

Answer

25 cm

Answer

50 cm

Question 2

Given a circle with center (2, 5) and radius 3 units, which of the following points lies on the circle?

Accepted Answer

(3, 6)

Answer

(5, 2)

Answer

(2, 8)

Answer

(1, 5)

Question 3

What is the name of a line that passes through the center of a circle?

Accepted Answer

Diameter

Answer

Tangent

Answer

Secant

Answer

Chord

Question 4

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

Accepted Answer

25π cm²

Answer

50π cm²

Answer

10π cm²

Question 5

What is the measure of the angle formed by two secants that intersect outside the circle? (Assume all angles are measured in degrees.)

Accepted Answer

Half the sum of the intercepted arcs

Answer

Half the difference of the intercepted arcs

Answer

The sum of the intercepted arcs

Answer

The difference of the intercepted arcs

Question 6

Which of the following is NOT a property of circles?

Accepted Answer

The area of a circle is proportional to the square of its diameter

Answer

All points on the circle are equidistant from the center

Answer

The diameter is twice the length of the radius

Answer

The circumference of a circle is proportional to its radius

Question 7

A sector of a circle has a central angle of 60 degrees and a radius of 10 cm. What is the area of the sector?

Accepted Answer

50π cm²

Answer

100π cm²

Answer

150π cm²

Answer

200π cm²

Question 8

Which of the following is a tangent to a circle?

Accepted Answer

A line that touches the circle at one point

Answer

A line that intersects the circle at two points

Answer

A line that passes through the center of the circle

Answer

A line that is parallel to the circle

Question 9

Which of the following is a sector of a circle?

Accepted Answer

A region bounded by two radii and an arc

Answer

A region bounded by a diameter and an arc

Answer

A region bounded by a chord and an arc

Answer

A region bounded by a tangent and an arc

Question 10

What is the ratio of the area of a sector to the area of the circle it belongs to?

Accepted Answer

Central angle / 360

Answer

Central angle / 180

Answer

Central angle / 90

Answer

Central angle / 45

Question 11

Which of these is NOT a property of tangents to circles?

Accepted Answer

They divide a circle into two equal halves.

Answer

They intersect a circle at one point.

Answer

They are perpendicular to the radius at the point of tangency.

Question 12

Determine the equation of a circle with a center at (2, 3) and a radius of 5.

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x + 2)² + (y + 3)² = 25

Question 13

Determine the radius of a circle given its circumference of 20π cm.

Accepted Answer

4 cm

Question 14

Identify the definition of a secant to a circle.

Accepted Answer

A line intersecting the circle at two distinct points.

Answer

A line that is tangent to the circle.

Question 15

Calculate the diameter of a circle with an area of 36π cm².

Accepted Answer

12 cm

Question 16

Determine the area of the sector formed by a central angle of 60° in a circle with a radius of 8 cm.

Accepted Answer

24π cm²

Answer

16π cm²

Question 17

A tangent to a circle is a line that:

Accepted Answer

touches the circle at exactly one point

Answer

intersects the circle at two points

Answer

intersects the circle at one point

Answer

lies inside the circle

Question 18

A secant to a circle is a line that:

Accepted Answer

intersects the circle at exactly two points

Answer

intersects the circle at one point

Answer

touches the circle at exactly one point

Answer

lies outside the circle

Question 19

The length of a tangent drawn from a point outside a circle to the center of the circle is equal to:

Accepted Answer

the sum of the radius and the distance from the point to the center of the circle

Answer

the radius of the circle

Answer

the diameter of the circle

Answer

the difference between the radius and the distance from the point to the center of the circle

Question 20

The sum of the measures of the interior angles of a cyclic quadrilateral is:

Accepted Answer

360°

Answer

180°

Answer

270°

Answer

540°

Question 21

What is the formula for the circumference of a circle with radius r?

Accepted Answer

2πr

Answer

πr

Answer

πr²

Answer

4πr²

Question 22

What is the area of a circle with radius r?

Accepted Answer

πr²

Answer

πr

Answer

2πr

Answer

4πr²

Question 23

What is the length of a tangent segment drawn from an external point to a circle?

Accepted Answer

The perpendicular distance from the point to the tangent line

Answer

The distance from the point to the center

Answer

The radius of the circle

Answer

The height of the triangle formed by the tangent, radius, and point

Question 24

If a sector of a circle has an area of 10π square units and a central angle of 120 degrees, what is the radius of the circle?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 25

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

Accepted Answer

2πr

Answer

πr²

Answer

πr

Answer

4πr

Question 26

A circle has a radius of 5 centimeters. What is its area? (Use π = 3.14)

Accepted Answer

78.5 cm²

Answer

20π cm²

Answer

10π cm²

Answer

50π cm²

Question 27

Which of the following describes an inscribed angle in a circle?

Accepted Answer

An angle formed by two chords with its vertex on the circle's circumference.

Answer

An angle with its vertex outside the circle and its sides intersecting the circle.

Answer

An angle formed by a tangent and a chord with its vertex on the circle.

Answer

An angle with its vertex inside the circle and its sides tangent to the circle.

Question 28

A circle has a radius of 5 inches. What is its area? (Use π = 3.14)

Accepted Answer

78.5 square inches

Answer

15.7 square inches

Answer

31.4 square inches

Answer

25 square inches

Question 29

A tangent line to a circle intersects the circle at how many points?

Accepted Answer

One

Answer

Two

Answer

Infinite

Answer

Zero

Question 30

A secant line intersects a circle at how many points?

Accepted Answer

Two

Answer

Infinite

Answer

Zero

Answer

One

Question 31

The radius of a circle is 7 cm. What is the length of its diameter?

Accepted Answer

14 cm

Answer

49 cm

Answer

3.5 cm

Answer

21 cm

Question 32

Two circles have the same center. What is this arrangement called?

Accepted Answer

Concentric circles

Answer

Secant circles

Answer

Tangent circles

Answer

Intersecting circles

Question 33

A line segment that passes through the center of a circle and connects two points on the circle's edge is known as a:

Accepted Answer

Diameter

Answer

Tangent

Answer

Radius

Answer

Chord

Question 34

A circle's radius measures 4 cm, and a chord drawn 3 cm from the center is given. Calculate the length of this chord:

Accepted Answer

6 cm

Answer

8 cm

Answer

10 cm

Answer

12 cm

Question 35

Given a circle with a 5-inch radius, determine its circumference:

Accepted Answer

10π inches

Answer

5π inches

Answer

25π inches

Answer

15π inches

Question 36

Calculate the area of a circle with a 10-centimeter diameter:

Accepted Answer

25π square centimeters

Answer

50π square centimeters

Answer

12.5π square centimeters

Answer

100π square centimeters

Question 37

Which of the following describes 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

Answer

A straight line that is parallel to the circle

Question 38

When two radii of a circle intersect at a point on the circle's circumference, what is the angle formed by these two radii?

Accepted Answer

90 degrees

Answer

60 degrees

Answer

180 degrees

Answer

120 degrees

Question 39

A secant intersects a circle with a 6-unit radius at a distance of 2 units from the center. Find the length of this secant:

Accepted Answer

8 units

Answer

4 units

Answer

12 units

Answer

10 units

Question 40

Calculate the area of a circle sector with a radius of 6 and a central angle of 45 degrees:

Accepted Answer

9π square units

Answer

18π square units

Answer

6π square units

Answer

12π square units

Question 41

What is the length of an arc in a circle with a radius of 5 and a central angle of 120 degrees?

Accepted Answer

5π/3 units

Answer

5π/6 units

Answer

10π/6 units

Answer

10π/3 units

Question 42

Write the equation of a circle with a center at (0, 0) and a radius of 3:

Accepted Answer

x² + y² = 9

Answer

(x + 3)² + (y + 3)² = 9

Answer

x - y = 3

Answer

y = 3x

Question 43

What is the radius of the circle inscribed in a square with side length 6?

Accepted Answer

3

Answer

6

Answer

12

Answer

1.5

Question 44

What is the area of the largest rectangle that can be inscribed in a circle with radius 5?

Accepted Answer

50 square units

Answer

125 square units

Answer

100 square units

Answer

25 square units

Question 45

A circle has a diameter of 12 cm. What is its circumference?

Accepted Answer

37.68 cm

Answer

75.36 cm

Answer

18.84 cm

Answer

113.04 cm

Question 46

A circular garden has a radius of 5 meters. If you want to build a fence around it, how many meters of fencing material will you need?

Accepted Answer

31.4 meters

Answer

15.7 meters

Answer

78.5 meters

Answer

157 meters

Question 47

The diameter of a bicycle wheel is 26 inches. How far will the bicycle travel if the wheel makes one complete revolution?

Accepted Answer

81.64 inches

Answer

208 inches

Answer

163.28 inches

Answer

52 inches

Question 48

A circle has an area of 153.86 square centimeters. What is its radius?

Accepted Answer

7 cm

Answer

14 cm

Answer

3.5 cm

Answer

49 cm

Question 49

A circular swimming pool has a diameter of 10 meters. What is the area of its surface?

Accepted Answer

78.5 square meters

Answer

157 square meters

Answer

31.4 square meters

Answer

314 square meters

Question 50

Line AB is tangent to circle O at point C. If the radius of circle O is 5 cm and line segment AB is 12 cm, what is the length of line segment OC?

Accepted Answer

5 cm

Answer

13 cm

Answer

12 cm

Answer

6 cm

Question 51

A line segment connecting two points on a circle and passing through the center is called a:

Accepted Answer

Diameter

Answer

Radius

Answer

Secant

Answer

Chord

Question 52

Two circles intersect at exactly one point. These circles are called:

Accepted Answer

Tangent circles

Answer

Similar circles

Answer

Congruent circles

Answer

Concentric circles

Question 53

A secant line intersects a circle at how many points?

Accepted Answer

Two

Answer

One

Answer

Three

Answer

Infinite

Question 54

A pizza has a diameter of 12 inches. It is cut into 8 equal slices. What is the area of one slice?

Accepted Answer

14.13 square inches

Answer

113.04 square inches

Answer

56.52 square inches

Answer

452.16 square inches