1. The radius of a circle is:
Answer:
Explanation:
Radius is a segment whose endpoints are the center and a point on the circle.
2. A chord of a circle that passes through the center is called:
Answer:
Explanation:
A diameter is a special chord that passes through the center, dividing the circle into two equal parts.
3. The number of tangents that can be drawn from an external point to a circle is:
Answer:
Explanation:
From an external point, two tangents can be drawn to a circle.
4. The perpendicular drawn from the center of a circle to a chord:
Answer:
Explanation:
The perpendicular from the center of a circle to a chord bisects the chord.
5. A circle can have ____ diameters.
Answer:
Explanation:
A circle can have infinite diameters as it can pass through the center in infinite ways.
6. The distance between the center of a circle and its chord AB is 4 cm. If the length of AB is 8 cm, then the radius of the circle is:
Answer:
Explanation:
Using the Pythagoras theorem in the right triangle formed, radius = √(AB/2)^2 + 4^2 = 5 cm.
7. A sector of a circle is the region between:
Answer:
Explanation:
A sector is bounded by two radii and the arc between them.
8. A line that touches the circle at exactly one point is called:
Answer:
Explanation:
A tangent touches the circle at only one point without cutting it.
9. The common point of a tangent and the circle is called:
Answer:
Explanation:
The point where a tangent touches the circle is called the point of contact.
10. The angle between the tangent at a point on the circle and the radius through the point is always:
Answer:
Explanation:
The radius at the point of contact is always perpendicular to the tangent.
11. The circle with the maximum area among all the circles with the same circumference is:
Answer:
Explanation:
Among all shapes with a given perimeter, a circle has the maximum area.
12. Equal chords of a circle subtend ____ angles at the center.
Answer:
Explanation:
Equal chords of a circle subtend equal angles at the center.
13. The length of a chord of a circle is 10 cm and its distance from the center is 4 cm. The radius of the circle is:
Answer:
Explanation:
Using Pythagoras theorem in the right triangle formed, radius = √(chord/2)^2 + 4^2 = 8.2 cm.
14. The chord of a circle, which is twice as long as its radius, subtends an angle of:
Answer:
Explanation:
In such a case, the angle subtended by the chord at the center of the circle is 60°.
15. Two circles touching each other externally touch at:
Answer:
Explanation:
Two circles touching each other externally will touch at exactly one point.
16. The distance between the centers of two circles touching each other externally is:
Answer:
Explanation:
The distance between their centers will be the sum of their radii.
17. In a circle of radius 14 cm, an arc subtends an angle of 60° at the center. The length of the arc is:
Answer:
Explanation:
Length of the arc = (60/360) × 2π × 14 = 14π/3 cm.
18. If a circle is divided into three equal arcs, each arc will subtend ____ angle at the center.
Answer:
Explanation:
Each arc will subtend 1/3 of 360°, which is 120°.
19. If two circles touch internally, the point of contact lies:
Answer:
Explanation:
For two circles touching internally, the point of contact lies on the circumference of the smaller circle.
20. The number of tangents that can be drawn to a circle from a point on the circle is:
Answer:
Explanation:
No tangent can be drawn from a point lying on the circle.