Q. A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
9 cm
Show solution
Solution
Using Pythagoras theorem, r² = (3)² + (4)² = 9 + 16 = 25. Thus, r = 5 cm.
Correct Answer:
B
— 7 cm
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Q. A circle has a circumference of 31.4 cm. What is its radius? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Circumference = 2πr. Thus, r = Circumference/(2π) = 31.4/(2π) = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If a circle has an area of 50π cm², what is its diameter? (2020)
A.
10 cm
B.
20 cm
C.
5 cm
D.
15 cm
Show solution
Solution
Area = πr², so r² = 50. Thus, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 14.14 cm.
Correct Answer:
A
— 10 cm
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Q. If a circle's radius is doubled, how does its area change? (2020)
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
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Solution
Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple the original area.
Correct Answer:
D
— It quadruples
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Q. If the area of a circle is 50π cm², what is the diameter? (2022)
A.
10 cm
B.
20 cm
C.
25 cm
D.
15 cm
Show solution
Solution
Area = πr² = 50π. Thus, r² = 50, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 20 cm.
Correct Answer:
B
— 20 cm
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Q. If the center of a circle is at (3, 4) and it passes through the point (7, 1), what is the radius? (2019)
A.
5 units
B.
4 units
C.
3 units
D.
6 units
Show solution
Solution
Radius = distance from center to point = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. If the diameter of a circle is 12 cm, what is the circumference? (2019)
A.
12π cm
B.
24π cm
C.
6π cm
D.
36π cm
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Solution
Circumference = πd = π(12) = 12π cm.
Correct Answer:
B
— 24π cm
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Q. If the diameter of a circle is 20 cm, what is the circumference? (2019)
A.
20π cm
B.
40π cm
C.
10π cm
D.
30π cm
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Solution
Circumference = πd = π(20) = 20π cm.
Correct Answer:
B
— 40π cm
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Q. If the diameter of a circle is increased by 50%, what is the percentage increase in the area of the circle? (2021)
A.
50%
B.
75%
C.
100%
D.
125%
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Solution
If diameter increases by 50%, radius increases by 25%. Area increases by (new area - old area)/old area = (1.25² - 1) × 100% = 56.25%.
Correct Answer:
C
— 100%
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Q. If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
The maximum radius of each circle can be half the distance between the centers, which is 10 cm.
Correct Answer:
B
— 10 cm
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Q. The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)
A.
50%
B.
75%
C.
100%
D.
125%
Show solution
Solution
If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.
Correct Answer:
C
— 100%
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Q. Two circles have radii of 3 cm and 4 cm. What is the distance between their centers if they are externally tangent? (2022)
A.
7 cm
B.
1 cm
C.
12 cm
D.
5 cm
Show solution
Solution
The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.
Correct Answer:
A
— 7 cm
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Q. Two circles touch each other externally. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers? (2023)
A.
8 cm
B.
2 cm
C.
15 cm
D.
10 cm
Show solution
Solution
Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.
Correct Answer:
A
— 8 cm
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Q. Two circles with radii 3 cm and 4 cm are externally tangent. What is the distance between their centers? (2022)
A.
7 cm
B.
1 cm
C.
12 cm
D.
5 cm
Show solution
Solution
The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.
Correct Answer:
A
— 7 cm
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Q. Two circles with radii 5 cm and 3 cm are externally tangent. What is the distance between their centers? (2023)
A.
8 cm
B.
10 cm
C.
6 cm
D.
5 cm
Show solution
Solution
Distance between centers = r1 + r2 = 5 cm + 3 cm = 8 cm.
Correct Answer:
A
— 8 cm
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Q. What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)
A.
25π cm²
B.
50π cm²
C.
100π cm²
D.
75π cm²
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Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. What is the area of a sector of a circle with radius 6 cm and a central angle of 90 degrees? (2023)
A.
9π cm²
B.
12π cm²
C.
18π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 6² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
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Q. What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
A.
9π cm²
B.
12π cm²
C.
18π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
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Q. What is the equation of a circle with center at (2, -3) and radius 4? (2022)
A.
(x-2)² + (y+3)² = 16
B.
(x+2)² + (y-3)² = 16
C.
(x-2)² + (y-3)² = 16
D.
(x+2)² + (y+3)² = 16
Show solution
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=4. Thus, (x-2)² + (y+3)² = 16.
Correct Answer:
A
— (x-2)² + (y+3)² = 16
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Q. What is the equation of a circle with center at (3, -2) and radius 4? (2023)
A.
(x-3)² + (y+2)² = 16
B.
(x+3)² + (y-2)² = 16
C.
(x-3)² + (y-2)² = 16
D.
(x+3)² + (y+2)² = 16
Show solution
Solution
The standard equation of a circle is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=4. Thus, (x-3)² + (y+2)² = 16.
Correct Answer:
A
— (x-3)² + (y+2)² = 16
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Q. What is the equation of a circle with center at (3, -2) and radius 5? (2022)
A.
(x-3)² + (y+2)² = 25
B.
(x+3)² + (y-2)² = 25
C.
(x-3)² + (y-2)² = 25
D.
(x+3)² + (y+2)² = 25
Show solution
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=5, so (x-3)² + (y+2)² = 25.
Correct Answer:
A
— (x-3)² + (y+2)² = 25
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Q. What is the length of an arc of a circle with a radius of 7 cm and a central angle of 60 degrees? (2023)
A.
7π/3 cm
B.
14π/3 cm
C.
14 cm
D.
21 cm
Show solution
Solution
Arc length = (θ/360) × 2πr = (60/360) × 2π(7) = (1/6) × 14π = 7π/3 cm.
Correct Answer:
A
— 7π/3 cm
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Q. What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
A.
5π/3 cm
B.
5π/6 cm
C.
5π/12 cm
D.
5π/4 cm
Show solution
Solution
Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 cm.
Correct Answer:
B
— 5π/6 cm
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Q. What is the length of the diameter of a circle with an area of 50π square units? (2023)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr². Given area = 50π, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.
Correct Answer:
A
— 10 units
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