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Class 6 Maths · Chapter 8: Playing with Constructions · NCERT Ganita Prakash section 8.1

Learn

Zoya is making a greeting card. She wants a perfect round sun in the corner. She ties a string to a pencil, holds the other end still with her finger, and swings the pencil round. Every point of the line is the same distance from her finger. That shape is a circle.

The fixed point is the centre. The distance from the centre to the circle is the radius. A compass does the same job as the string: open it to the radius, put the sharp point on the centre, and turn.

Part of a circle is an arc. For the card's border, Zoya draws half circles of radius 1 cm along a line, one up and one down. Each half circle uses up 2 cm (one diameter) of the line, so a line 8 cm long holds 4 of them.

8 ÷ 2 = 4 half circles

Circles of the same radius make beautiful patterns. Draw one circle, then put the compass point anywhere on it and draw another of the same radius. Keep going round: you get a flower!

Explore: your compass board. Open the compass, then tap a dot to draw.

  1. Draw a circle of radius 2 cm with centre O.
  2. Draw the circle with centre O that passes through A.
  3. Draw a circle of radius 1.5 cm with centre P.

Remember

  • All points of a circle are the same distance (the radius) from its centre.
  • A compass draws circles and arcs. The diameter is 2 × the radius.

Quick check

A circle has radius 4 cm. Point K is 4 cm from the centre. Where is K?

  1. On the circle
  2. Inside the circle
  3. Outside the circle
  4. At the centre
Answer

On the circle. Every point exactly one radius from the centre lies on the circle.

Think about it

Imagine all the points that are exactly 3 cm from a point P. What shape do they make? What about all the points that are less than 3 cm from P?

One answer

The points exactly 3 cm away form a circle of radius 3 cm around P. The points less than 3 cm away fill the inside of that circle.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.