Circles: Properties, Equations, and Theorems

Question 1

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

Accepted Answer

Side

Answer

Center

Answer

Radius

Answer

Diameter

Question 2

What is the area of a circle with radius 'r'?

Accepted Answer

πr²

Answer

πr

Answer

2πr

Answer

4πr²

Question 3

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

Accepted Answer

5 cm

Answer

25 cm

Answer

10 cm

Answer

20 cm

Question 4

If two circles are tangent externally, what is the distance between their centers?

Accepted Answer

Sum of their radii

Answer

Difference of their radii

Answer

Twice the radius of the larger circle

Answer

Half the radius of the smaller circle

Question 5

Which of the following is NOT a theorem related to circles?

Accepted Answer

Pythagorean Theorem

Answer

Inscribed Angle Theorem

Answer

Intercept Theorem

Answer

Angle Bisector Theorem

Question 6

If a circle is inscribed in a square with a side length of 10 cm, what is the ratio of the area of the circle to the area of the square?

Accepted Answer

π/4

Answer

1/2

Answer

1/4

Answer

π/2

Question 7

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

Accepted Answer

Rectangle

Answer

Radius

Answer

Diameter

Answer

Chord

Question 8

Which theorem states that the area of a circle is equal to πr²?

Accepted Answer

Area of a Circle Theorem

Answer

Pythagorean Theorem

Answer

Circumference of a Circle Theorem

Answer

Diameter of a Circle Theorem

Question 9

In a circle, which line segment connects two points on the circle and passes through the center?

Accepted Answer

Diameter

Answer

Chord

Answer

Tangent

Answer

Secant

Question 10

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

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 11

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 - 2)² + (y - 3)² = 5

Answer

(x + 2)² + (y + 3)² = 5

Question 12

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

Accepted Answer

Square

Answer

Radius

Answer

Diameter

Answer

Chord

Question 13

A circle with a radius of 5 cm has a circumference of:

Accepted Answer

25π cm

Answer

5 cm

Answer

10 cm

Answer

50π cm

Question 14

A circle has an equation of (x - 3)² + (y + 2)² = 25. What is the center of the circle?

Accepted Answer

(3, 2)

Answer

(3, -2)

Answer

(-3, 2)

Answer

(-3, -2)

Question 15

Which of the following transformations will not produce a circle?

Accepted Answer

Expansion

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 16

What is the name of the point that is equidistant from all points on a circle?

Accepted Answer

Center

Answer

Origin

Answer

Radius

Answer

Diameter

Question 17

Which of the following formulas is used to calculate the circumference of a circle?

Accepted Answer

C = 2πr

Answer

A = πr²

Answer

D = πd

Answer

V = ⅓πr³

Question 18

What is the name of the line segment that passes through the center of a circle and connects two points on the circle?

Accepted Answer

Diameter

Answer

Radius

Answer

Chord

Answer

Tangent

Question 19

If a circle has a radius of 5 centimeters, what is its area?

Accepted Answer

25π cm²

Answer

50π cm²

Answer

10π cm²

Answer

100π cm²

Question 20

Which of the following is NOT a theorem related to circles?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Inscribed Angle Theorem

Answer

Tangent-Secant Theorem

Question 21

Two circles are tangent to each other if they

Accepted Answer

Intersect at one point

Answer

Intersect at two points

Answer

Do not intersect at all

Answer

Overlap completely

Question 22

What is the measure of an inscribed angle that intercepts a semicircle?

Accepted Answer

180°

Answer

30°

Answer

60°

Answer

90°

Question 23

A line is tangent to a circle if it

Accepted Answer

Is perpendicular to the radius of the circle at the point of contact

Answer

Intersects the circle at two points

Answer

Passes through the center of the circle

Answer

Is parallel to the radius of the circle

Question 24

In a circle, what is the fixed point called?

Accepted Answer

Center

Answer

Radius

Answer

Diameter

Answer

Chord

Question 25

The formula for calculating the circumference of a circle is:

Accepted Answer

C = 2πr

Answer

C = πr

Answer

C = r^2π

Answer

C = 4πr

Question 26

Which of the following theorems is related to circles?

Accepted Answer

Circle Inscribed in a Triangle Theorem

Answer

Pythagorean Theorem

Answer

Angle Bisector Theorem

Answer

Parallel Line Theorem

Question 27

Which of the following is true about a chord of a circle?

Accepted Answer

It connects any two points on the circle

Answer

It always passes through the center of the circle

Answer

It is perpendicular to the radius of the circle

Answer

It divides the circle into two equal parts

Question 28

What is the standard equation of a circle?

Accepted Answer

x^2 + y^2 = r^2

Answer

x^2 - y^2 = r^2

Answer

y^2 - x^2 = r^2

Answer

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

Question 29

A sector of a circle has a radius of 6 units and a central angle of 90 degrees. What is the area of the sector?

Accepted Answer

12π square units

Answer

9π square units

Answer

18π square units

Answer

27π square units

Question 30

What formula represents the circumference of a circle?

Accepted Answer

2πr

Answer

πr

Answer

r2

Answer

2r

Question 31

What is the definition of a circle?

Accepted Answer

A two-dimensional figure with curved sides that is equidistant from a fixed point called the center

Answer

A three-dimensional figure with flat surfaces

Answer

A shape with no straight lines

Answer

A figure with only one side

Question 32

What is the term for the distance around the outside edge of a circle?

Accepted Answer

Circumference

Answer

Diameter

Answer

Radius

Answer

Area

Question 33

What is the name of the line segment that passes through the center of a circle and connects two points on the circle?

Accepted Answer

Diameter

Answer

Radius

Answer

Chord

Answer

Secant

Question 34

Which of the following formulas can be used to calculate the area of a circle?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πd

Answer

A = πd²

Question 35

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

Accepted Answer

The circumference of a circle is always less than its diameter.

Answer

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

Answer

A circle has only one center.

Answer

A circle can be divided into equal parts called sectors.

Question 36

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

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 37

What is the area of a circle with a diameter of 14 cm?

Accepted Answer

98π cm²

Answer

49π cm²

Answer

147π cm²

Answer

196π cm²

Question 38

What is the name of the point in the center of a circle?

Accepted Answer

Center

Answer

Radius

Answer

Chord

Answer

Tangent

Question 39

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

Accepted Answer

Area

Answer

Radius

Answer

Diameter

Answer

Chord

Question 40

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

Accepted Answer

C = 2πr

Answer

C = πr

Answer

C = πd

Answer

C = 2πd

Question 41

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

Accepted Answer

25π cm²

Answer

50π cm²

Answer

100π cm²

Answer

250π cm²

Question 42

Which property describes tangent lines to a circle?

Accepted Answer

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

Answer

They intersect the circle at one point.

Answer

They pass through the center of the circle.

Answer

They are parallel to the diameter of the circle.

Question 43

Which theorem is related to circles?

Accepted Answer

Inscribed angle theorem

Answer

Exterior angle theorem

Answer

Alternate interior angle theorem

Answer

Corresponding angles theorem

Question 44

A circle is a two-dimensional figure enclosed by a curved line. What is this curved line called?

Accepted Answer

(C) Circumference

Answer

(A) Radius

Answer

(B) Diameter

Answer

(D) Chord

Question 45

The formula for calculating the circumference of a circle is:

Accepted Answer

(A) 2πr

Answer

(B) πr^2

Answer

(C) 4πr^2

Answer

(D) r^2π

Question 46

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

Accepted Answer

(C) A circle has four right angles.

Answer

(A) All points on the circle are the same distance from the center.

Answer

(B) The diameter of a circle is twice the length of the radius.

Answer

(D) A chord of a circle can intersect the circle at two points.

Question 47

The equation of a circle with center (h, k) and radius r is:

Accepted Answer

(A) (x - h)² + (y - k)² = r²

Answer

(B) (x - h)² - (y - k)² = r²

Answer

(C) (x - k)² + (y - h)² = r²

Answer

(D) (x - k)² - (y - h)² = r²

Question 48

A circle has a circumference of 28π cm. What is its radius?

Accepted Answer

(B) 7 cm

Answer

(A) 4 cm

Answer

(C) 14 cm

Answer

(D) 28 cm

Question 49

Which of the following is a theorem related to circles?

Accepted Answer

(B) Circle Tangent Theorem

Answer

(A) Pythagorean Theorem

Answer

(C) Triangle Sum Theorem

Answer

(D) Law of Sines

Question 50

A sector of a circle is the region bounded by two radii and:

Accepted Answer

(B) An arc

Answer

(A) A diameter

Answer

(C) A chord

Answer

(D) A tangent

Question 51

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

Accepted Answer

(x - 2)² + (y + 3)² = 16

Answer

(x)² + (y)² = 16

Answer

x + y = 16

Answer

x² - y² = 16

Question 52

Which theorem states that the tangent to a circle is perpendicular to the radius drawn to the point of tangency?

Accepted Answer

Circle Tangent Theorem

Answer

Pythagorean Theorem

Answer

Tangent Theorem

Answer

Inscribed Angle Theorem

Question 53

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 intersects the circle at one point

Answer

A line that is tangent to the circle

Answer

A line that passes through the center of the circle