NCERT Solutions for Class 5th Maths Chapter 7 Two diameters and the shape they make — Play with Circles
Book page 101 Updated on2026-09-19
Q1.
Do you remember a circle? (a) Draw a circle with a compass and mark its centre. (b) Draw its diameter. Mark the endpoints of the diameter. (c) Draw another diameter of the circle and mark the endpoints. (d) Now join the four points. What shape is formed? Check the sides of the quadrilateral and the angles obtained.
Answer
A rectangle is formed. Its opposite sides are equal and all four of its angles are right angles.
Do it step by step
Draw the circle with your compass and mark the centre O with a dot.
Draw one diameter. A diameter is a straight line that goes right through the centre and touches the circle at both ends. Call its ends A and C.
Draw a second diameter, slanting differently. Call its ends B and D.
Join A to B, B to C, C to D, and D back to A.
Measure. AB comes out equal to CD, and BC equal to DA. Check each corner with the corner of a sheet of paper — all four are right angles.
The four endpoints always join up into a rectangle, whichever pair of diameters you choose.
Why it is always a rectangle: Look at the two dotted lines — they are the diagonals of the quadrilateral. Both are diameters, so they are exactly the same length. And both pass through the centre, which cuts each one exactly in half. A four-sided shape whose two diagonals are equal and cut each other in half is always a rectangle.
Another way to see it: All four points A, B, C and D are the same distance (the radius) from the centre O. So the centre is exactly in the middle of the shape, and the shape must be perfectly balanced — that balance is what makes the right angles.
Q2.
Try with a different pair of diameters. What do you notice about the shape that is formed?The circle on page 101 — two diameters drawn, and the four endpoints joined.
Answer
You get a rectangle every single time. Only the size and slant of the rectangle change, never the kind of shape.
How the two diameters cross
Shape you get
At a sharp angle (a narrow cross)
A long, thin rectangle
At a wider angle
A shorter, fatter rectangle
At a right angle (a plus sign)
A square — which is a special rectangle
Turn one diameter and the rectangle changes shape. Turn it to a right angle and you get a square.
Why the answer never changes: The reason from the last question does not depend on how you draw the diameters. Any two diameters are the same length and each cuts the other in half at the centre. Those two facts alone force the shape to be a rectangle.
Special case worth remembering: When the two diameters cross at a right angle, all four sides become equal and the rectangle becomes a square.
Q3.
Is it possible to create a 4-sided shape other than a rectangle through this process?
Answer
No. Joining the ends of two diameters always gives a rectangle.
Why no other shape can appear
The two diameters are the diagonals of the shape you draw.
Every diameter of a circle is the same length. So the two diagonals are equal.
Every diameter passes through the centre, and the centre is its middle point. So each diagonal cuts the other exactly in half.
Equal diagonals that cut each other in half — that is the mark of a rectangle, and of nothing else.
Diagonal 1 = Diagonal 2 (both are diameters) Each is cut in half at O → the shape is a rectangle If the diagonals also cross at a right angle → a square
What would you need for other shapes? A kite needs diagonals that are not equal. A general parallelogram needs diagonals that are not equal either. Since the circle only ever gives you equal diagonals, you can never make those shapes this way.
Try it and see: Draw five different pairs of diameters in five circles and join the ends each time. Every one of them will be a rectangle. That is a small piece of mathematics you discovered yourself.