## 1. If a line intersects a circle at two distinct points, then it is called a:

### Answer:

### Explanation:

A line that intersects a circle at two distinct points is termed as a secant.

## 2. The number of tangents that can be drawn to a circle from an external point is:

### Answer:

### Explanation:

From an external point, two tangents can be drawn to a circle.

## 3. The tangent to a circle is ________ to the radius at the point of contact.

### Answer:

### Explanation:

The radius at the point of contact is always perpendicular to the tangent of the circle.

## 4. If a chord and a tangent intersect externally, then the product of the lengths of the two segments of the chord is:

### Answer:

### Explanation:

If PT is the tangent and PQ, PR are two segments of the chord, then PQ × PR = PT².

## 5. The angle between the tangent at a point on a circle and the chord drawn from that point is equal to:

### Answer:

### Explanation:

This is a property of the circle which relates the angle between the tangent and the chord to the angle subtended by the chord at the center.

## 11. If two circles intersect at two points, the line passing through these points is called:

### Answer:

### Explanation:

When two circles intersect at two points, the line segment joining these points is called the common chord of the two circles.

## 12. The angle subtended by an arc at the center is ________ the angle subtended by it at any point on the remaining part of the circle.

### Answer:

### Explanation:

This is known as the Angle at the Center Theorem. The angle subtended by an arc at the center is twice the angle subtended by it at any other point on the circle.

## 13. If a line segment joining two points on a circle is extended beyond the circle, it intersects the:

### Answer:

### Explanation:

When extended beyond the circle, the chord becomes a secant.

## 14. The locus of a point equidistant from a given point is:

### Answer:

### Explanation:

A circle is defined as the locus of all points equidistant from a fixed point (the center).

## 15. In a circle, if a chord is nearer to the center, then its corresponding arc is:

### Answer:

### Explanation:

Chords closer to the center subtend larger arcs.

## 16. A tangent and a radius when extended meet at:

### Answer:

### Explanation:

A tangent to a circle is perpendicular to the radius through the point of contact.

## 17. The distance between the center of a circle and a chord AB is 4 cm. If the radius of the circle is 5 cm, then the length of AB is:

### Answer:

### Explanation:

Using the Pythagorean theorem, AB = 2√(r^2 – d^2) = 6 cm where r is the radius and d is the distance from the center to the chord.

## 18. If two chords AB and CD of a circle are equal, then the measure of ∠AOB is ________ the measure of ∠COD.

### Answer:

### Explanation:

Equal chords of a circle subtend equal angles at the center.

## 19. The area of a sector of a circle with a radius of 7 cm and angle 60° is:

### Answer:

### Explanation:

Area = (angle/360) × π × r^2 = 154/3 cm^2.

## 20. A circle with no endpoints is termed as:

### Answer:

### Explanation:

An arc is a part of the circumference of a circle without endpoints.