Question

How can we draw a circle with a given line a diameter, without actually measuring the line?

Answer 1

We are given a line as the diameter of the circle and we need to draw a circle without actually measuring the line.

By constructing the perpendicular bisector of the diameter, we can find the centre of the circle and using the centre we can draw a circle.

The steps of construction are as follows:

1) Draw a line segment AB of any length. This line AB is the diameter of the circle.

2) Take radius more than half the length of AB and mark arcs on the upper and lower sides of AB by taking A and B as the centres. Name the points of intersection as C and D.

3) Join CD and name the point on which it cuts AB as E. E is the centre of the required circle.

4) With E as the centre and radius as EB = EA as the centre, draw a circle.

Thus, the required circle is drawn above.