Q1. 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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Q2. What is the relationship between the lengths of two tangents drawn from an external point to a circle?
Solution:
The lengths of two tangents drawn from an external point to a circle are equal.
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Q3. In a circle, if two chords AB and CD are equal in length, what can be said about their distances from the center?
Solution:
If two chords are equal in length, they are equidistant from the center of the circle.
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Q4. If the diameter of a circle is 10 cm, what is the circumference of the circle?
Solution:
The circumference of a circle is given by the formula C = πd. For d = 10 cm, C = π(10) ≈ 31.4 cm.
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Q5. 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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Q6. What is the measure of the central angle that subtends an arc of 120 degrees in a circle?
Solution:
The measure of the central angle is equal to the measure of the arc it subtends, which is 120 degrees.
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Q7. 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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Q8. If two chords in a circle are equal in length, what can be said about their distances from the center of the circle?
Solution:
If two chords in a circle are equal in length, they are equidistant from the center of the circle.
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Q9. If two tangents are drawn from an external point to a circle, what can be said about the lengths of the tangents?
Solution:
The lengths of the tangents drawn from an external point to a circle are equal.
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Q10. If a tangent and a chord intersect at a point on the circle, what is the relationship between the angle formed and the angle subtended by the chord at the opposite arc?
Solution:
The angle formed by the tangent and the chord is equal to the angle subtended by the chord at the opposite arc.
