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Q1. If a circle has a radius of 7 cm, what is the area of the circle?
Solution:
The area of a circle is given by the formula A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
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Q2. In a circle, if two chords AB and CD intersect at point E, which of the following is true?
Solution:
According to the intersecting chords theorem, the products of the segments of the chords are equal, hence AE * EB = CE * ED.
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Q3. In a circle, if the radius is doubled, what happens to the area of the circle?
Solution:
The area of a circle is given by A = πr². If the radius is doubled, the new area becomes π(2r)² = 4πr², which is four times the original area.
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Q4. If the radius of a circle is doubled, how does the area of the circle change?
Solution:
The area of a circle is given by A = πr². If the radius is doubled (r' = 2r), the new area A' = π(2r)² = 4πr², which is four times the original area.
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Q5. If the diameter of a circle is 14 cm, what is the circumference of the circle?
Solution:
The circumference C of a circle is given by C = πd. Here, d = 14 cm, so C = π * 14 ≈ 43.98 cm, which rounds to 44 cm.
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Q6. In a circle, if the diameter is 14 cm, what is the circumference of the circle?
Solution:
The circumference of a circle is given by C = πd. Thus, C = π(14) ≈ 43.96 cm.
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Q7. If two circles intersect at points A and B, which of the following statements is true regarding the angles formed?
Solution:
The angles subtended by the same arc at the circumference are equal, hence angle ACB = angle APB.
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Q8. In a circle, if the radius is 5 cm, what is the length of an arc that subtends a central angle of 60 degrees?
Solution:
The length of an arc is given by L = (θ/360) * 2πr. Thus, L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
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Q9. If a tangent from point P touches the circle at point T, which of the following statements is true?
Solution:
The tangent to a circle at any point is perpendicular to the radius drawn to the point of tangency.
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Q10. In triangle ABC, if angle A is 50 degrees and angle B is 70 degrees, what is the measure of angle C?
Solution:
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 70) = 60 degrees.
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