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NCERT Solutions for Class 7th Maths Chapter 7 Visualising the construction of circles — In-text Questions

Book page 155 Updated on2026-09-19

Q1.
Does a triangle exist with sidelengths 4 cm, 5 cm and 8 cm? This satisfies the triangle inequality: 8 < 4 + 5 = 9. Why do we not need to check the other two sides?
Answer

Because the other two comparisons are already guaranteed by the size order.

4 < 5 + 8 = 13 ✓ (4 is smaller than 8 alone)
5 < 4 + 8 = 12 ✓ (5 is smaller than 8 alone)
8 < 4 + 5 = 9 ✓ — the only comparison that could have failed
Why it happens: Each of the smaller lengths is already less than the longest length by itself; adding a third positive length can only widen the gap. So checking the longest against the sum of the other two settles the whole question.
Q2.
Now, suppose that a circle of radius 5 cm is constructed, centred at B. Can you draw a rough diagram of the resulting figure?
4 cm8 cmAXB
Page 155 — the circle of radius 4 cm centred at A, drawn on the base AB = 8 cm; X is the point where it cuts AB.
Answer

Take AB = 8 cm as the base. Draw the circle of radius 4 cm about A and the circle of radius 5 cm about B — they overlap in a lens-shaped region.

A B X 4 cm 4 cm circle A, r = 4 circle B, r = 5
AB = 8 cm, AX = 4 cm so BX = 4 cm, which is less than the 5 cm radius of circle B.
Tip: Draw the base first and mark X, the point where circle A cuts AB. Then you can see at a glance whether circle B swallows X or not.
Q3.
Note that in the figure below, AX = 4 cm and AB = 8 cm. So, what is BX? Does this length help in visualising the resulting figure?
4 cm8 cmAXB
Page 155 — the circle of radius 4 cm centred at A, drawn on the base AB = 8 cm; X is the point where it cuts AB.
Answer

BX = 4 cm, and it settles the whole picture.

BX = AB – AX
= 8 cm – 4 cm
= 4 cm
Radius of the circle centred at B = 5 cm
BX = 4 cm < 5 cm
So X lies inside circle B
Why it happens: X is the point of circle A that is nearest to B. If even this nearest point is inside circle B, then part of circle A is inside circle B and part of it (the far side) is outside — so the two circles must cross, and they cross at exactly two points. Either of those points together with A and B gives a triangle. Hence a triangle with sides 4 cm, 5 cm and 8 cm does exist.
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