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NCERT Solutions Ganita Prakash Chapter 8 Figure it Out — Artwork

Book page 191 Updated on2026-09-05

Q1.
What radius should be taken in the compass to get this half circle? What should be the length of AX?
Answer

The two waves must be identical, so the central line AB = 8 cm is shared equally between them.

AX = XB = 8 ÷ 2 = 4 cm
AX is the diameter of the first half circle
radius = 4 ÷ 2 = 2 cm

Answer: radius = 2 cm and AX = 4 cm. The tip of the compass is placed at the mid-point of AX, that is 2 cm from A.

Why: a half circle stands on its diameter. Here the half circle starts at A and ends at X, so AX itself is the diameter, and the radius is always half the diameter.
Q2.
Take a central line of a different length and try to draw the wave on it.
Answer

The method never changes — only the numbers change. Take, for example, AB = 10 cm.

  1. Draw AB = 10 cm and mark the mid-point X, so AX = XB = 5 cm.
  2. Radius needed = 5 ÷ 2 = 2.5 cm.
  3. Place the tip 2.5 cm from A and draw the half circle above AB, from A to X.
  4. Place the tip 2.5 cm from X and draw the half circle below AB, from X to B.
Central line ABAX = XBRadius of each half circle
8 cm4 cm2 cm
10 cm5 cm2.5 cm
12 cm6 cm3 cm
6 cm3 cm1.5 cm
Tip: the radius is always one quarter of the central line — AB ÷ 4. Check: 8 ÷ 4 = 2, 10 ÷ 4 = 2.5, 12 ÷ 4 = 3. ✔
Q3.
Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure, ‘A Person’). The challenge here is to get both the waves to be identical. This may be tricky!
Answer

A wave smaller than a half circle means the arc is flatter. For that the compass tip is not put on the line AB but away from it, and a bigger radius is used.

Steps of construction

  1. Draw AB = 8 cm and mark the mid-point X (AX = XB = 4 cm).
  2. Take a radius bigger than 2 cm — say 2.5 cm — in the compass.
  3. Place the tip below the line, on the perpendicular through the mid-point of AX, and adjust it until the pencil passes through both A and X. Draw the arc above AB.
  4. Do not change the compass opening. Now place the tip above the line, on the perpendicular through the mid-point of XB, until the pencil passes through X and B. Draw that arc below AB.
A X B tip below tip above
Flatter waves. The same compass opening is used for both arcs, and the two tips are placed at equal distances on opposite sides of AB — that is what makes the waves identical.
Why both waves come out identical: two arcs are identical when they have the same radius and the same chord. Here both chords are 4 cm (AX and XB) and the compass opening is never changed, so the two arcs must match exactly. The trick is only to remember to put the tip on the opposite side of the line the second time.
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