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
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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 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. 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
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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 circumference?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
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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 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%
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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.
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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
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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 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.
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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.
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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 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 is used to describe a line that touches a circle at exactly one point?
A.
Chord
B.
Diameter
C.
Tangent
D.
Secant
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Solution
A tangent is defined as a line that touches a circle at exactly one point.
Correct Answer: C — Tangent
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