NCERT Solutions for Class 7th Maths Chapter 6 A Pointed Arch — Figure it Out
Book page 151 Updated on2026-09-19
Q1.
Use support lines in Fig. 6.11 to construct a pointed arch. Make different arches, by changing the radius of the arcs.
Fig. 6.11, page 150 — the two support lines, with their midpoints marked.
Answer
Keep the two supporting segments fixed and change only where the arc centres sit on their perpendicular bisectors.
Where the centre is placed
Radius
Arch you get
Far out along the perpendicular bisector
large
Almost straight sides — a sharp, tall arch
Moderately out
medium
A gentle, classic pointed arch
Close to the midpoint
small
Strongly bulging sides — a plump arch
Draw the two equal supporting segments PT and QT.
Construct the perpendicular bisector of PT and of QT.
Pick a centre on the bisector of PT; open the compass from that centre to P; sweep the arc from P up to T.
Use the same distance from the midpoint on the other side, and sweep the arc from Q to T.
Change the distance and repeat for a new arch.
Why it happens: the two endpoints of each arc are locked by the supporting segments, so the arc can only vary in how much it curves. Curvature is decided by the radius alone — small radius, sharp curve; large radius, gentle curve. Everything else stays put.
Q2.
Make your own arch designs.
Answer
Start from a symmetric frame, then decide how many lobes and which way each arc curves.
Frame first. Draw the base AD, construct equal angles at A and D, and cut equal lengths. Draw the axis (the perpendicular bisector of AD) — every arc must be mirrored across it.
Choose the lobes. One big arc gives a plain round arch. Three arcs give a trefoil. Five give a cinquefoil.
Choose the curvature. Arcs bulging outwards give a full, rounded look; arcs bulging inwards (inflexed arcs) give the elegant ogee of Mughal architecture.
Mirror everything. For every arc on the left, draw its partner on the right with the same radius.
Ink the outline in colour and rub out all supporting lines and centres.
Why it happens: every good arch design is the same two decisions repeated — where the arc starts and ends (fixed by the frame) and how much it bends (fixed by the radius). Mirroring across the axis is what keeps the design from looking accidental.
Try This: look at a doorway, a temple gopuram or a mosque arch near your home. Sketch its outline and try to guess where the mason put the centres of the arcs.