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Knowledge Desk
Greeks including Euclid, the father of geometry were good at geometrical construction but Greeks could
not easily do arithmetic. They had only whole numbers without zero and negative numbers. This meant
they could not, for example, divide 5 by 2 and get 2.5, because 2.5 is not a whole number. So, faced with the
problem of finding the midpoint of a line, they could not do the obvious – measure it and divide by 2. They
had to have other ways, leading to the constructions using compass and straightedge or rulers. Euclid and
the Greeks solved problems graphically, by drawing shapes instead of applying arithmetic.

To draw a square inscribed by a given circle

1. With centre O, draw a circle of any radius, say R.
2. Through the centre O, draw a diameter, say AC.
3. Draw another diameter BD passing through point O and perpendicular to diameter AC with
the help of protractor.

4. Join A to B, B to C, C to D and D to A, with the help of a ruler.

5. ABCD is the required square.
D D

R R R
O A O C A O C

B B
Practice Time 8D

1. Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°.
What do you observe about the sides?
2. Construct a rectangle one of whose sides is 5 cm and the diagonal is of length 10 cm.

3. Mark two points P and Q 7 cm apart from each other in your notebook. Now locate points X and Y
which are equidistant (6 cm) from P and Q.
4. All sides of a 4-sided figure are equal in length. Suppose two sides inclined at an angle are drawn as
follows. Mark the fourth point D to complete the figure. Discuss the idea you used in construction.
A
4 cm

B

4 cm
C
5. Construct a house in which all the sides are of length 4 cm.
6. Inscribe a square in a circle with a diameter of 80 mm.

247 Playing with Constructions