Page 225 - Ganit Kaushal

Was it necessary to draw two full circles to get the points C and D, whereas we only needed a small
part of both the circles?

Yes, you are right! There is no need to draw two full circles to get points C and D. We can have just
the small arcs of two circles passing through C and D.
Therefore, we can rewrite Step 3 as follows:

Step 3: Taking A as the centre and using a radius more than half of AB, draw two C
small arcs — one above and one below the line segment AB. Likewise, taking point B
as the centre and with the same radius, draw two small arcs, one above and one below O
the line AB to cut the previous arcs at points C and D. Join CD. Mark the point as O A B
where it cuts the line AB. CD is the required perpendicular bisector of AB, and O is D
the midpoint of AB (see adjoining figure).

CAN YOU THINK?

Is the perpendicular bisector of a line joining two points the line of symmetry (LoS) of the figure
obtained in step 3?
Ans, Yes, it is. Isn’t it?

Exercise 8.1

1. Draw a circle of radius 3.7 cm.
2. Draw two circles of radii 3.9 cm and 3.1 cm having the same centre O.

3. Draw any circle and any two of its diameters. If you join the ends of these diameters, what figure is
obtained? What figure is obtained if the diameters are perpendicular to each other? Check by drawing
it.
4. Draw a line segment AB of length 8 cm. With A as the centre, draw a circle of radius 5 cm and with
B as the centre, draw another circle of radius 3 cm. What do you observe?
5. Construct a circle of radius 3.8 cm and draw the following in it.
(a) centre O (b) diameter PQ

(c) radius OA (d) chord AB Note
A chord of a circle is a line segment
6. Draw a line segment of length 8.6 cm and construct its joining any two points on the
perpendicular bisector. circumference that is not a diameter.
7. With AB of length 5.8 cm as the diameter, draw a circle.

8. Draw a circle with centre P and radius 3.3 cm. Draw any chord AB. Construct the perpendicular bisector
of AB and examine if it passes through P.
9. Draw a circle of radius 4.2 cm. Draw any two of its chords. Construct the perpendicular bisectors of
these chords. Where do these bisectors meet?
10. Let A and B be the centres of two circles of equal radii; draw them so that each one of them passes
through the centre of the other. Let them intersect at C and D. Examine whether AB and CD are
perpendicular to each other.

11. Construct a line segment of length 7.5 centimetres using a ruler and a compass.

Playing with Constructions 223