Page 233 - Ganit Kaushal

6. Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What
do you say about the sides of such a rectangle?

7. Construct a square of side 6 cm. Draw a circle of radius 3 cm inside the square whose centre is the
same as the centre of the square. Does this circle touch the square from the inside? If yes, at how many
points? If you join all these points of contact, what shape do you get?

8. Give the lengths of the sides of a rectangle that cannot be divided into two identical squares. Also,
give reasons for your answer. (NCERT)
9. Give the lengths of the sides of a rectangle that cannot be divided into three identical squares. Give

reasons for your answer. (NCERT)
10. Draw a rectangle with sides of length 8 cm and 6 cm. Now, draw a circle with radius 5 cm and centre
at the centre of the rectangle. Does the circle pass through the vertices of the rectangle?

8.7 POINTS EQUIDISTANT FROM TWO GIVEN POINTS

Suppose two points are given some distance apart. How can we locate a point which is equidistant from these
two given points? Let us learn this with the help of the following construction. C

Construction 11: Suppose two points A and B are 6 cm apart. Locate a point C that is 8 cm
away from both points A and B. 8 cm 8 cm

(This construction is very similar to construction 4. The only difference is that here we
know the distance of point C from A and B. We will first draw a rough diagram, marking
all measurements as shown in the adjoining figure.) A 6 cm B

Sol. Step 1: Draw a line AB, 6 cm long using a ruler and pencil. (see figure (i)) A 6 cm B
(i)
Step 2: Set a distance of 8 cm between the legs of a compass. (see figure (ii))
Step 3: Without changing the setting of the compass, put the pointer at A and draw an arc. Now, put the
pointer of the compass at B and draw another arc to cut the previous arc at point C. (See the adjoining
figure (iii)). After completing step 3, we get figure (iv).

Step 4: Join AC and BC with the help of a ruler and pencil. We get the following required figure (v).

C C C

A 6 cm B A 6 cm B A 6 cm B
(ii) (iii) (iv) (v)
After completing the construction, readers are advised to measure the distances AC and BC.

Are they both equal? Is AC = BC = 8 cm?

Yes, it is. Excellent!

Playing with Constructions 231