## 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.