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Definition of a Circle

A circle is the set of all points in a plane that are at the same distance from a fixed point called the centre. This fixed distance is called the radius.

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Student-friendly explanation

Think of the centre as the fixed point and the radius as the equal distance rule. Every point on the boundary follows this rule. A diameter is a chord passing through the centre and its length is twice the radius.

How to write this in exams

  1. 1

    Start with the exact idea

    A circle is the set of all points in a plane that are at the same distance from a fixed point called the centre. This fixed distance is called the radius.

  2. 2

    Then show how to use it

    First locate the centre. Then identify whether the given segment touches the centre. If it joins centre to boundary, it is a radius; if it passes through centre joining two boundary points, it is a diameter.

  3. 3

    Add one concrete example

    If O is the centre and radius is 5 cm, then every point P on the circle has OP = 5 cm. A diameter of this circle is 10 cm.

  4. 4

    Avoid this incomplete answer

    Writing radius as 14 cm when diameter is 14 cm is wrong because radius is only half the diameter.

Definition

A circle is the set of all points in a plane that are at the same distance from a fixed point called the centre. This fixed distance is called the radius.

Example

If O is the centre and radius is 5 cm, then every point P on the circle has OP = 5 cm. A diameter of this circle is 10 cm.

Rule to remember

Radius: distance from centre to any point on the circle. Diameter = 2 x radius. Radius = diameter / 2.

Memory hook

Same distance from centre means circle.

Examples and method

Worked example

A circle has diameter 14 cm. Radius = 14 / 2 = 7 cm. So any point on the circle is 7 cm from the centre.

Method to apply

First locate the centre. Then identify whether the given segment touches the centre. If it joins centre to boundary, it is a radius; if it passes through centre joining two boundary points, it is a diameter.

Diagram support

Draw centre O, a point P on the circle, radius OP, and a diameter AB through O. Mark OA = OB.

How CBSE asks it

Questions may ask students to identify radius, diameter, chord, centre, or use diameter = 2r in a figure-based problem.

Avoid common mistakes

Common confusion

Students often call the full circular region a circle. In school geometry, the circle usually means the boundary, while the region inside is the circular region or disc.

Common wrong answer

Writing radius as 14 cm when diameter is 14 cm is wrong because radius is only half the diameter.

Exam tip

When a radius is drawn to a point on the circle, immediately mark it equal to every other radius from the same centre.

Quick check

If AB is a diameter of a circle with centre O and OA = 4 cm, what is AB?

AB is 8 cm because a diameter is twice the radius, and OA is one radius of length 4 cm.

Answer writing and exam use

1-mark answer

A circle is the set of all points in a plane that are at the same distance from a fixed point called the centre. This fixed distance is called the radius.

2-mark answer

A circle is the set of all points in a plane that are at the same distance from a fixed point called the centre. This fixed distance is called the radius. Radius: distance from centre to any point on the circle. Diameter = 2 x radius. Radius = diameter / 2. If O is the centre and radius is 5 cm, then every point P on the circle has OP = 5 cm. A diameter of this circle is 10 cm.

3-mark answer

Think of the centre as the fixed point and the radius as the equal distance rule. Every point on the boundary follows this rule. A diameter is a chord passing through the centre and its length is twice the radius. Radius: distance from centre to any point on the circle. Diameter = 2 x radius. Radius = diameter / 2. A circle has diameter 14 cm. Radius = 14 / 2 = 7 cm. So any point on the circle is 7 cm from the centre. Questions may ask students to identify radius, diameter, chord, centre, or use diameter = 2r in a figure-based problem. Writing radius as 14 cm when diameter is 14 cm is wrong because radius is only half the diameter.
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