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Q1. 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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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. If a circle has a diameter of 10 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. Here, r = 5 cm, so L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
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Q4. 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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Q5. 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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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 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.
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Q8. If a tangent from point P touches a circle at point T, what is the relationship between the radius OT and the tangent PT?
Solution:
The radius drawn to the point of tangency is perpendicular to the tangent line at that point.
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Q9. 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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Q10. 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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