EN हिं

NCERT Solutions Ganita Prakash Chapter 8 & 216Hints A) Eyes and B) the four equal sides — Hints

Book page 215 Updated on2026-09-05

Q1.
A) Eyes. Points A and B are the locations where the tip of the compass is placed when drawing the curves of the eye. Note that the upper curve and the lower curve should together form a symmetrical figure. For this to happen, where should these points A and B be placed? Make a good estimate.
Answer

A and B must be placed on the perpendicular through the middle of the eye, one above and one below, and at equal distances from the line joining the two corners of the eye.

  • Draw the two light horizontal helper lines and mark the two corners of the eye on the middle line.
  • Find the mid-point of the corner-to-corner segment and draw a perpendicular through it.
  • Mark A on this perpendicular above the eye, and B the same distance below it.
  • Use the same compass opening for both curves: from B for the upper curve, from A for the lower one.
Why this makes the eye symmetrical: a curve is the mirror image of another when their centres are mirror images and their radii are equal. Putting A and B at equal distances on opposite sides of the horizontal line makes them mirror images, so the upper and lower curves match perfectly and meet at the two corners.
Tip: bringing A and B closer to the eye makes it fatter; moving them further away makes it a thin, sleepy eye. Try both and pick the one you like — it may take several trials.
Q2.
B) For the purpose of construction, let us take the side lengths to be of 5 cm. We need to identify only one more point to make this a 4-sided figure. That point, let us call it D, should be 5 cm from both B and C. How can such a point be found? Can any of the ideas used in the ‘House’ problem be used here?
Answer

Yes — it is exactly the ‘House’ idea. The apex A of the house was the point 5 cm from both B and C; here D is the point 5 cm from both B and C.

  1. Open the compass to 5 cm.
  2. Place the tip at B and draw an arc on the far side of BC.
  3. Without changing the opening, place the tip at C and draw another arc crossing the first.
  4. Their crossing point is D. Join BD and CD.
BD = 5 cm (D is on the arc centred at B)
CD = 5 cm (D is on the arc centred at C)
with AB = AC = 5 cm, all four sides of ABDC are 5 cm
Why one point is all that is missing: three of the four corners (A, B and C) are already fixed by the two 5 cm segments. The fourth corner has only two conditions to meet — 5 cm from B and 5 cm from C — and two arcs settle both at once. The figure that results is a rhombus, which answers question 3 of page 215.
Was this helpful? Report an error