Draw a circle with centre at point $O$. Draw its two chords $AB$ and $CD$ such that $AB$ is not parallel to $CD$. Draw the perpendicular bisectors of $AB$ and $CD$. At what point do they intersect?

Given:

A circle with centre at point $O$. 

To do:

We have to draw its two chords $AB$ and $CD$ such that $AB$ is not parallel to $CD$ and the perpendicular bisectors of $AB$ and $CD$. 

Solution:

Steps of construction:

(i) Draw a circle with centre $O$ and a suitable radius.

(ii) Draw two chords $AB$ and $CD$ which are not parallel to each other.

(iii) Draw the perpendicular bisectors of $AB$ and $CD$ with the help of a ruler and compasses.

The two chords intersect each other at the centre $O$ of the circle.