Q1. What is the relationship between the angles subtended by the same arc at the center and on the circumference of a circle?
Solution:
The angle subtended at the center of a circle is always twice the angle subtended at the circumference by the same arc.
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Q2. 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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Q3. 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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Q4. If a circle has a radius of 5 cm, what is the area of the circle?
Solution:
The area of a circle is given by the formula A = πr². Thus, A = π(5)² = 25π cm².
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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. 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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Q7. If two circles intersect at points A and B, and the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?
Solution:
The perpendicular from the center of a circle to a chord bisects the chord.
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Q8. 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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Q9. 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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Q10. If two triangles are similar, which of the following is true about their corresponding sides?
Solution:
In similar triangles, the corresponding sides are proportional to each other.
