Q. If a circle has a circumference of 62.8 cm, what is its diameter?
A.
10 cm
B.
20 cm
C.
30 cm
D.
40 cm
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Solution
Using the formula C = πd, we find d = C/π = 62.8/3.14 = 20 cm.
Correct Answer:
B
— 20 cm
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Q. If a circle has a radius of 10 cm, what is the length of an arc that subtends a central angle of 90 degrees?
A.
15.7 cm
B.
25 cm
C.
17.5 cm
D.
20 cm
Show solution
Solution
The length of an arc is given by L = (θ/360) * 2πr. Here, L = (90/360) * 2π(10) = 17.5 cm.
Correct Answer:
C
— 17.5 cm
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Q. If a circle has a radius of 7 cm, what is its area? (2020)
A.
154 cm²
B.
49 cm²
C.
28 cm²
D.
14 cm²
Show solution
Solution
The area of a circle is calculated using A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
Correct Answer:
A
— 154 cm²
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Q. If the circumference of a circle is 31.4 cm, what is the radius?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the radius of a circle is increased by 50%, what happens to the area of the circle?
A.
It increases by 50%.
B.
It increases by 100%.
C.
It increases by 125%.
D.
It increases by 150%.
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Solution
If the radius increases by 50%, the new radius is 1.5r, and the area becomes (1.5r)² = 2.25r², which is a 125% increase.
Correct Answer:
C
— It increases by 125%.
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Q. If two circles intersect at two points, what can be said about their centers?
A.
They are the same.
B.
They are equidistant from the intersection points.
C.
They lie on the same line.
D.
They are at a fixed distance apart.
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Solution
The centers of two intersecting circles are equidistant from the points of intersection.
Correct Answer:
B
— They are equidistant from the intersection points.
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Q. If two circles intersect at two points, what can be said about their relationship?
A.
They are concentric.
B.
They are tangent to each other.
C.
They are secant to each other.
D.
They do not intersect.
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Solution
Circles that intersect at two points are said to be secant to each other.
Correct Answer:
C
— They are secant to each other.
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Q. If two circles intersect at two points, which of the following statements is true? (2021)
A.
The centers of the circles are equidistant from the intersection points.
B.
The line joining the centers of the circles passes through the intersection points.
C.
The circles are tangent to each other.
D.
The area of intersection is always a triangle.
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Solution
The centers of the circles are equidistant from the intersection points, making option 0 true.
Correct Answer:
A
— The centers of the circles are equidistant from the intersection points.
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Q. In a circle, if a chord is drawn, which of the following statements is true regarding the angles formed?
A.
The angles subtended by the chord at the center are equal.
B.
The angles subtended by the chord at the circumference are equal.
C.
The angles subtended at the center are half of those at the circumference.
D.
The angles subtended at the circumference are equal to those at the center.
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Solution
The angles subtended by the same chord at the circumference are equal.
Correct Answer:
B
— The angles subtended by the chord at the circumference are equal.
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Q. In a circle, if a chord is perpendicular to a radius at its endpoint, what can be inferred about the chord?
A.
It is the longest chord.
B.
It bisects the circle.
C.
It is a diameter.
D.
It is bisected by the radius.
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Solution
A radius that is perpendicular to a chord at its endpoint bisects the chord.
Correct Answer:
D
— It is bisected by the radius.
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Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the circumference?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the remaining part of the circle?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is the angle in radians subtended by the arc at the center? (2021)
A.
1 rad
B.
2 rad
C.
3 rad
D.
4 rad
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Solution
The angle in radians is given by the formula θ = s/r, where s is the arc length. Thus, θ = 10/5 = 2 rad.
Correct Answer:
B
— 2 rad
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Q. In a circle, if the radius is doubled, how does the area change?
A.
It remains the same.
B.
It doubles.
C.
It quadruples.
D.
It increases by a factor of eight.
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Solution
If the radius is doubled, the area increases by a factor of four (since area is proportional to the square of the radius).
Correct Answer:
C
— It quadruples.
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Q. In a circle, if the radius is increased by 50%, what happens to the area of the circle?
A.
It increases by 50%
B.
It doubles
C.
It increases by 125%
D.
It increases by 75%
Show solution
Solution
If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.
Correct Answer:
C
— It increases by 125%
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Q. In a circle, if the radius is increased by 50%, what happens to the area?
A.
Increases by 25%
B.
Increases by 50%
C.
Increases by 75%
D.
Increases by 125%
Show solution
Solution
If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.
Correct Answer:
D
— Increases by 125%
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Q. In the context of geometry, which of the following statements about circles is true?
A.
A circle is defined by its radius alone.
B.
The diameter of a circle is twice the radius.
C.
All points on a circle are equidistant from the center.
D.
A circle can have more than one center.
Show solution
Solution
The diameter of a circle is indeed twice the radius, making this statement true.
Correct Answer:
B
— The diameter of a circle is twice the radius.
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Q. What is the area of a circle with a radius of 7 cm?
A.
154 cm²
B.
49 cm²
C.
28 cm²
D.
100 cm²
Show solution
Solution
The area of a circle is given by A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
Correct Answer:
A
— 154 cm²
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Q. What is the relationship between the angles formed by two intersecting chords in a circle?
A.
They are always equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are proportional to the lengths of the chords.
Show solution
Solution
The angles formed by two intersecting chords are supplementary.
Correct Answer:
B
— They are supplementary.
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Q. What is the relationship between the angles subtended by the same arc at the center and at the circumference of a circle?
A.
They are equal.
B.
The angle at the center is twice that at the circumference.
C.
The angle at the circumference is twice that at the center.
D.
They are complementary.
Show solution
Solution
The angle subtended at the center is always twice that subtended at the circumference.
Correct Answer:
B
— The angle at the center is twice that at the circumference.
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Q. What is the relationship between the radius and the area of a circle? (2022)
A.
Area is directly proportional to the radius.
B.
Area is inversely proportional to the radius.
C.
Area is proportional to the square of the radius.
D.
Area is independent of the radius.
Show solution
Solution
The area of a circle is given by A = πr², indicating that area is proportional to the square of the radius.
Correct Answer:
C
— Area is proportional to the square of the radius.
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Q. What is the relationship between the radius and the chord length in a circle?
A.
Chords are always longer than the radius.
B.
Chords can be equal to the radius.
C.
Chords can be shorter than the radius.
D.
All of the above.
Show solution
Solution
Chords can vary in length and can be longer, equal to, or shorter than the radius.
Correct Answer:
D
— All of the above.
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Q. What is the relationship between the radius and the diameter of a circle?
A.
The radius is half of the diameter.
B.
The diameter is half of the radius.
C.
The radius and diameter are equal.
D.
The diameter is the sum of two radii.
Show solution
Solution
The radius is defined as half of the diameter.
Correct Answer:
A
— The radius is half of the diameter.
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Q. Which of the following best describes the relationship between a circle and a tangent line?
A.
A tangent line intersects the circle at two points.
B.
A tangent line is perpendicular to the radius at the point of contact.
C.
A tangent line can be drawn from any point inside the circle.
D.
A tangent line passes through the center of the circle.
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Solution
A tangent line is defined as a line that touches the circle at exactly one point and is perpendicular to the radius at that point.
Correct Answer:
B
— A tangent line is perpendicular to the radius at the point of contact.
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Q. Which of the following is NOT a property of a circle?
A.
All radii are equal.
B.
The diameter is the longest chord.
C.
A circle has a finite area.
D.
A circle can have corners.
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Solution
A circle is defined as a round shape with no corners.
Correct Answer:
D
— A circle can have corners.
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Q. Which of the following terms describes a line that touches a circle at exactly one point? (2023)
A.
Chord
B.
Diameter
C.
Tangent
D.
Secant
Show solution
Solution
A line that touches a circle at exactly one point is called a tangent.
Correct Answer:
C
— Tangent
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Q. Which of the following terms is used to describe a line that touches a circle at exactly one point?
A.
Chord
B.
Diameter
C.
Tangent
D.
Secant
Show solution
Solution
A tangent is defined as a line that touches a circle at exactly one point.
Correct Answer:
C
— Tangent
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Q. Which of the following terms refers to a line segment that connects two points on a circle?
A.
Diameter
B.
Chord
C.
Tangent
D.
Secant
Show solution
Solution
A chord is defined as a line segment whose endpoints lie on the circle.
Correct Answer:
B
— Chord
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