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)
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A.
5 cm
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B.
7 cm
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C.
10 cm
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D.
9 cm
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)
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A.
5 cm
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B.
10 cm
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C.
15 cm
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D.
20 cm
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's radius is doubled, how does its area change? (2020)
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A.
It remains the same
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B.
It doubles
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C.
It triples
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D.
It quadruples
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 diameter of a circle is 12 cm, what is the circumference? (2019)
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A.
12π cm
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B.
24π cm
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C.
6π cm
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D.
36π cm
Solution
Circumference = πd = π(12) = 12π cm.
Correct Answer: B — 24π cm
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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)
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A.
7 cm
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B.
1 cm
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C.
12 cm
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D.
5 cm
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. What is the equation of a circle with center at (3, -2) and radius 5? (2022)
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A.
(x-3)² + (y+2)² = 25
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B.
(x+3)² + (y-2)² = 25
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C.
(x-3)² + (y-2)² = 25
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D.
(x+3)² + (y+2)² = 25
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 the diameter of a circle with an area of 50π square units? (2023)
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A.
10 units
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B.
5 units
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C.
20 units
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D.
15 units
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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