NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.4

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A circle is a closed plane figure consisting of all those points of the plane which are at a constant distance from a fixed point.
The fixed point is called the centre of the circle and the constant distance is known as the radius of the circle.
If O is the centre of the circle and OM = r is the radius of the circle.
If N is another point on the circle, then the line segment ON is another radius of the circle. All the radii of the circle have one end point common, which is the centre of the circle. Also, OM = ON = r.
Thus, all radii of a circle are equal.

A line segment passing through the centre of a circle and having its end points on the circle, is called diameter of the circle.
If, PQ is a diameter of the circle having its centre at O. Also, OP and OQ are two radii of the circle.
So OP = OQ, because O is the mid-point of PQ.
Thus, the centre of a circle bisects a diameter into two equal parts.
Hence, Diameter = 2 × Radius

Just as we can draw an infinite number of radii through the centre of a circle, we can draw an infinite number of diameters.
As observed earlier, the centre O of a circle is the mid-point of every diameter of circle. Thus, the diameters of a circle are concurrent and the common point is the centre of the circle.

Consider a circle with centre O and radius r. This circle divides the plane into three parts:

1. The part of the plane, consisting of those points P, for which OP < r, is called the interior of the circle, with centre O and radius r. In other words, the set of all those points which lie inside the circle is known as its interior.
2. The part of the plane, consisting of those points P for which OP > r, is called the exterior of the circle, with centre O and radius r. In other words, the set of all those points which lie outside the circle is called the exterior of the circle.
3. The part of the plane, consisting of those points P, for which OP = r, is the circle itself, i.e., the set of all points lying on the circle is the circle itself.

Note: Clearly, the circle, its interior and exterior have no common point and together account for all points of the plane.
The part of the plane of the circle that consists of the circle and its interior is called the circular region.