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CraftExam
medium difficulty8 min

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.

In one line: Same distance from centre means circle.

Practice This Concept

Understand it

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.

Formula and rule

Radius: distance from centre to any point on the circle.

Diameter = 2 x radius.

Radius = diameter / 2.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A circle has diameter 14 cm.

  1. 1Radius = 14 / 2 = 7 cm.
  2. 2So any point on the circle is 7 cm from the centre.

Method you can reuse

  1. 1First locate the centre.
  2. 2Then identify whether the given segment touches the centre.
  3. 3If it joins centre to boundary, it is a radius; if it passes through centre joining two boundary points, it is a diameter.

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer
AB is 8 cm because a diameter is twice the radius, and OA is one radius of length 4 cm.

Common wrong answer

Writing radius as 14 cm when diameter is 14 cm.

Why it loses marks: Radius is only half the diameter.

Don't mix this up

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.

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.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask students to identify radius, diameter, chord, centre, or use diameter = 2r in a figure-based problem.
  1. 1

    Enough for 1 mark

    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

    Add for 2 marks

    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.

  3. 3

    Add for 3 marks

    Every point on the boundary follows this rule.

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