Circles: Master the Fundamentals of Geometry

Question 1

Which equation represents the circle with center (3, -2) and radius 5?

Accepted Answer

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

Answer

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

Answer

x^2 + y^2 - 6x + 4y + 3 = 0

Question 2

What is the area of a circle with a radius of 6 cm?

Accepted Answer

36π cm^2

Answer

12π cm^2

Answer

72π cm^2

Question 3

If two circles have radii of 5 cm and 12 cm, respectively, what is the ratio of their areas?

Accepted Answer

25:144

Answer

5:12

Answer

12:5

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$x^2 + y^2 - 2hx + 2ky = r^2$$

Question 5

Which of the following is a theorem related to circles?

Accepted Answer

Tangent-Secant Theorem

Answer

Pythagorean Theorem

Answer

Law of Sines

Answer

Law of Cosines

Question 6

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

Accepted Answer

It is bounded by two diameters

Answer

It is bounded by an arc

Answer

It is bounded by two radii

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 cm^2

Answer

100π cm^2

Answer

25π cm^2

Question 8

If a circle has a diameter of 14 cm, what is the length of its radius?

Accepted Answer

7 cm

Answer

14 cm

Answer

3.5 cm

Answer

28 cm

Question 9

Which of the following is a defining property of a circle?

Accepted Answer

All points on the circle are equidistant from the center.

Answer

It has no sides.

Answer

It has two axes of symmetry.

Answer

It is a regular polygon.

Question 10

A circle is inscribed in a square with side length 10. Find the radius of the circle.

Accepted Answer

5√2

Answer

10

Answer

25

Answer

5

Question 11

What is the area of a circle with a diameter of 12 centimeters?

Accepted Answer

36π cm^2

Answer

18π cm^2

Answer

12π cm^2

Question 12

Which of the following statements about the properties of a circle is NOT true?

Accepted Answer

All chords are equal in length.

Answer

All radii are equal in length.

Answer

The distance from any point on the circle to the center is constant.

Question 13

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

Accepted Answer

It has three sides.

Answer

It is a closed curve with smooth edges.

Answer

All points on the circle are equidistant from a fixed point (the center).

Question 14

Find the circumference of a circle with a radius of 7 centimeters.

Accepted Answer

14π centimeters

Answer

7π centimeters

Answer

49π centimeters

Answer

28π centimeters

Question 15

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

Accepted Answer

25π square centimeters

Answer

10π square centimeters

Answer

5π square centimeters

Question 16

Which of the following is 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 17

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

Accepted Answer

120 degrees

Answer

60 degrees

Answer

180 degrees

Question 18

Which of the following is a sector of a circle?

Accepted Answer

A region of a circle bounded by two radii and their intercepted arc.

Answer

A region of a circle bounded by two tangents and their intercepted arc.

Answer

A region of a circle bounded by a chord and an intercepted arc.

Question 19

Find the area of a sector with a central angle of 120 degrees in a circle with a radius of 7 centimeters.

Accepted Answer

21π/2 square centimeters

Answer

7π/2 square centimeters

Answer

28π/2 square centimeters

Answer

14π/2 square centimeters

Question 20

Which of the following is a theorem related to circles?

Accepted Answer

The angle inscribed in a semicircle is a right angle.

Answer

The sum of the interior angles of a circle is 180 degrees.

Answer

All circles are similar.

Answer

The area of a circle is equal to its circumference.