Question 1

A circle is the collection of all points in a plane which are at a constant distance from a fixed point. What is the fixed point called?

Accepted Answer

The fixed point is called the center of the circle. By definition, a circle is the locus of a point moving in a plane such that its distance from a fixed point (center) is always constant (radius).

Question 2

Equal chords of a circle subtend angles at the center.

Accepted Answer

Equal chords of a circle subtend equal angles at the center. This is a standard theorem in circle geometry stating that if two chords are equal in length, their corresponding central angles are also equal.

Question 3

The longest chord of a circle is always a:

Accepted Answer

The longest chord of a circle is its diameter, which passes through the center of the circle and divides it into two equal semicircles.

Question 4

Perpendicular from the center of a circle to a chord the chord.

Accepted Answer

The perpendicular drawn from the center of a circle to a chord bisects the chord. This is a fundamental theorem used extensively in solving geometric problems involving circles.

Question 5

Angle subtended by an arc at the center is the angle subtended by it at any point on the remaining part of the circle.

Accepted Answer

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

Circles — NCERT Class 9 Mathematics Important Questions & Revision Notes