Q1. If a circle has a radius of 4 cm, what is the area of the circle?
Solution:
The area A of a circle is given by A = πr². Therefore, A = π(4)² = 16π cm².
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Q2. In a circle, if two angles subtended by the same arc are equal, what can be concluded about those angles?
Solution:
Angles subtended by the same arc at the circumference of a circle are equal.
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Q3. Two circles are tangent to each other. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers?
Solution:
The distance between the centers of two tangent circles is the sum of their radii: 3 cm + 5 cm = 8 cm.
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Q4. What is the measure of the angle subtended by an arc at the center of a circle compared to the angle subtended at any point on the remaining part of the circle?
Solution:
The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the remaining part of the circle.
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Q5. What is the length of an arc of a circle with a radius of 5 cm that subtends an angle of 60 degrees at the center?
Solution:
The length of an arc is given by the formula L = (θ/360) * 2πr. For r = 5 cm and θ = 60°, L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
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Q6. In a circle, if a tangent is drawn from a point outside the circle, what is the relationship between the tangent and the radius at the point of contact?
Solution:
A tangent drawn from a point outside the circle is perpendicular to the radius at the point of contact.
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Q7. What is the relationship between the radius and the tangent at the point of contact on a circle?
Solution:
The radius drawn to the point of contact is always perpendicular to the tangent at that point.
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Q8. If a circle has a radius of 4 cm, what is the diameter of the circle?
Solution:
The diameter of a circle is twice the radius. For a radius of 4 cm, the diameter is 2 * 4 = 8 cm.
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Q9. In a circle, if a radius is drawn to a point where a tangent touches the circle, what is the angle between the radius and the tangent?
Solution:
The radius drawn to the point of tangency is perpendicular to the tangent, forming a 90-degree angle.
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Q10. If a tangent and a radius meet at a point on the circle, what is the angle between them?
Solution:
The tangent to a circle at any point is perpendicular to the radius at that point, forming a 90-degree angle.
