Circles: Interactive Quizzes and Practice Questions

Question 1

What is a defining characteristic of a tangent to a circle?

Accepted Answer

It is perpendicular to the radius drawn from the point of tangency.

Answer

It intersects the circle at two distinct points.

Answer

It passes through the center of the circle.

Question 2

The diameter of a circle is given as 12 cm. What is its radius?

Accepted Answer

6 cm

Answer

3 cm

Answer

24 cm

Answer

12 cm

Question 3

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

Accepted Answer

25π cm²

Answer

125π cm²

Answer

50π cm²

Answer

10π cm²

Question 4

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

Accepted Answer

It intersects the circle at two points

Answer

It lies outside the circle

Answer

It has the same length as the radius

Answer

It is perpendicular to the radius at the point of contact

Question 5

An inscribed angle intercepts an arc of 120°. What is the measure of this inscribed angle?

Accepted Answer

60°

Answer

30°

Answer

120°

Answer

90°

Question 6

Determine the length of the arc of a circle with a radius of 10 cm and a central angle of 60°.

Accepted Answer

10π/3 cm

Answer

10π cm

Answer

20π/3 cm

Answer

5π cm

Question 7

When two radii of a circle intersect at its center, what is the measure of the angle formed by these radii?

Accepted Answer

180°

Answer

360°

Answer

90°

Answer

270°

Question 8

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

Accepted Answer

10 cm

Answer

15 cm

Answer

20 cm

Answer

5 cm

Question 9

Two tangents to a circle are drawn from an external point. If one tangent is 10 cm in length, and the other tangent is 8 cm in length, what is the radius of the circle?

Accepted Answer

9 cm

Answer

18 cm

Answer

10 cm

Answer

11 cm

Question 10

What is the measure of an inscribed angle that intercepts an arc of 150 degrees?

Accepted Answer

75 degrees

Answer

90 degrees

Answer

150 degrees

Answer

30 degrees

Question 11

Two circles are congruent and have a radius of 5 cm. What is the distance between their centers if they are externally tangent?

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Question 12

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

Accepted Answer

10π cm

Answer

50 cm

Answer

25π cm

Answer

5π cm

Question 13

Identify the characteristic of a tangent to a circle.

Accepted Answer

Touches the circle at exactly one point.

Answer

Intersects the circle at two points.

Answer

Lies outside the circle.

Answer

Lies within the circle.

Question 14

Define a sector of a circle.

Accepted Answer

A region bounded by two radii and an arc

Answer

A region bounded by a chord and two radii

Answer

A region bounded by two chords and an arc

Answer

A region bounded by a diameter and an arc

Question 15

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

Accepted Answer

πr^2 cm²

Answer

πr cm²

Answer

4πr cm²

Answer

2πr cm²

Question 16

Calculate the perimeter of a semicircle with a radius of 6 cm.

Accepted Answer

6π cm + 12 cm

Answer

6π cm

Answer

12π cm

Answer

12 cm

Question 17

If a tangent to a circle is drawn from a point outside the circle, it is perpendicular to the:

Accepted Answer

radius from the point of tangency

Answer

diameter from the point of tangency

Answer

chord from the point of tangency

Answer

secant from the point of tangency

Question 18

If two chords of a circle intersect inside the circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the:

Accepted Answer

other chord

Answer

radius

Answer

tangent

Answer

diameter

Question 19

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

Accepted Answer

Its diameter is twice its circumference

Answer

Its radius is half its diameter

Answer

Its circumference is 2πr

Answer

Its area is πr²

Question 20

If a circle has a circumference of 16π cm, its area is:

Accepted Answer

64π cm²

Answer

8π cm²

Answer

16π cm²

Answer

32π cm²

Question 21

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

Accepted Answer

31.42 cm

Answer

15.71 cm

Answer

25 cm

Answer

78.54 cm

Question 22

A tangent to a circle is a line that intersects the circle at exactly one point. Which of the following statements is true about a tangent to a circle?

Accepted Answer

A tangent is perpendicular to the radius drawn to the point of contact.

Answer

A tangent is always parallel to the radius.

Answer

A tangent can intersect the circle at two points.

Question 23

The angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at a point on the circumference. What is the measure of the angle subtended at the center if the angle subtended at the circumference is 30°?

Accepted Answer

60°

Answer

30°

Answer

90°

Answer

15°

Question 24

A secant is a line that intersects a circle at two points. If a secant intersects a circle at points A and B, and point O is the center of the circle, what is the relationship between the angles ∠AOB and ∠ACB, where C is a point on the circumference between A and B?

Accepted Answer

∠AOB = 2∠ACB

Answer

∠AOB = 1/2∠ACB

Answer

There is no relationship between the angles.

Answer

∠AOB = ∠ACB

Question 25

A line segment joining two points on a circle is called a _____.

Accepted Answer

Chord

Answer

Diameter

Answer

Radius

Answer

Tangent

Question 26

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

Accepted Answer

One

Answer

Infinite

Answer

Two

Question 27

A chord of a circle subtends an angle of 60 degrees at the center. What is the measure of the minor arc intercepted by the chord?

Accepted Answer

60 degrees

Answer

180 degrees

Answer

30 degrees

Answer

120 degrees

Question 28

Two circles intersect at two points. The line segment joining the points of intersection is called a:

Accepted Answer

Common chord

Answer

Tangent

Answer

Radius

Answer

Diameter

Question 29

The angle between a tangent and a radius drawn to the point of contact is:

Accepted Answer

90 degrees

Answer

45 degrees

Answer

0 degrees

Answer

180 degrees

Question 30

A sector of a circle with central angle 120 degrees has an area of 15π square units. What is the radius of the circle?

Accepted Answer

5 units

Answer

15 units

Answer

10 units

Answer

3 units

Question 31

The angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference. This statement describes:

Accepted Answer

The Inscribed Angle Theorem

Answer

The Tangent-Chord Theorem

Answer

The Pythagorean Theorem

Answer

The Intersecting Chords Theorem

Question 32

If two chords of a circle intersect inside the circle, then the product of the segments of one chord is equal to the product of the segments of the other chord. This theorem is known as:

Accepted Answer

The Intersecting Chords Theorem

Answer

The Tangent-Chord Theorem

Answer

The Inscribed Angle Theorem

Answer

The Pythagorean Theorem

Question 33

A circle is inscribed in a triangle. What is the relationship between the incenter of the circle and the angles of the triangle?

Accepted Answer

The incenter is the intersection of the angle bisectors of the triangle.

Answer

The incenter is the center of the circumcircle of the triangle.

Answer

The incenter is the midpoint of the longest side of the triangle.

Question 34

A circle is circumscribed about a triangle. What is the relationship between the circumcenter of the circle and the sides of the triangle?

Accepted Answer

The circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle.

Answer

The circumcenter is the intersection of the altitudes of the triangle.

Answer

The circumcenter is the intersection of the medians of the triangle.

Question 35

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

Accepted Answer

31.42 cm

Answer

25 cm

Answer

15.71 cm

Answer

78.54 cm

Question 36

A tangent line is drawn to a circle at point P. Which of the following is true about the angle between the tangent line and the radius drawn to point P?

Accepted Answer

It is a right angle (90 degrees)

Answer

It can be any angle

Answer

It is an acute angle

Answer

It is an obtuse angle

Question 37

Two chords of a circle intersect inside the circle. What is the relationship between the angles formed by the intersection?

Accepted Answer

The opposite angles are equal

Answer

The angles are supplementary

Answer

The adjacent angles are equal

Answer

The angles are complementary

Question 38

A sector of a circle has a central angle of 60 degrees. If the radius of the circle is 10 cm, what is the area of the sector?

Accepted Answer

52.36 cm²

Answer

31.42 cm²

Answer

104.72 cm²

Answer

157.08 cm²

Question 39

A circle has a diameter of 12 cm. What is the area of the circle?

Accepted Answer

113.10 cm²

Answer

37.68 cm²

Answer

56.55 cm²

Answer

226.20 cm²

Question 40

A secant line intersects a circle at points A and B. If the length of AB is 10 cm and the distance from the center of the circle to the midpoint of AB is 3 cm, what is the radius of the circle?

Accepted Answer

5 cm

Answer

7 cm

Answer

3 cm

Answer

10 cm

Question 41

Two tangents are drawn to a circle from an external point. What is the relationship between the lengths of the tangents?

Accepted Answer

They are equal

Answer

They are inversely proportional

Answer

They are proportional

Answer

There is no relationship

Question 42

An arc of a circle has a central angle of 120 degrees. If the circumference of the circle is 24 cm, what is the length of the arc?

Accepted Answer

8 cm

Answer

4 cm

Answer

6 cm

Answer

12 cm

Question 43

A circle is inscribed in a triangle. What is the relationship between the sides of the triangle and the points of tangency?

Accepted Answer

The segments of the sides of the triangle between the points of tangency and the vertices are equal.

Answer

The segments of the sides are proportional

Answer

The segments are inversely proportional

Question 44

A quadrilateral is circumscribed around a circle. What is the relationship between the lengths of its opposite sides?

Accepted Answer

The sum of the lengths of opposite sides is equal

Answer

There is no relationship

Answer

The opposite sides are equal

Answer

The opposite sides are proportional