Draw a circle with centre $ \mathrm{C} $ and radius $ 3.4 \mathrm{~cm} $. Draw any chord $ \overline{\mathrm{AB}} $. Construct the perpendicular bisector of $ \overline{\mathrm{AB}} $ and examine if it passes through $ \mathrm{C} $.

To do:

We have to construct the perpendicular bisector of $\overline{AB}$ and examine if it passes through $C$.

Solution:

Steps of construction:

(i) Let us draw a circle with centre $C$ and radius $3.4\ cm$.

(ii) Now, let us draw any chord on the circle with centre $C$ and point the intersection of the chord with the circle as $A$ and $B$ respectively.

(iii) Now, let us draw two arcs by taking $A$ and $B$ as centres above $\overline{AB}$ and let us point the point of intersection of two arcs as $D$.

(iv) Similarly let us draw two arcs by taking $A$ and $B$ as centres below $\overline{AB}$  and let us point the point of intersection of two arcs as $E$.

(v) Now, let us join the points $E$ and $D$.

(vi) Therefore, $\overline{DE}$ is the perpendicular bisectors of $\overline{AB}$ and when $\overline{DE}$ is extended it passes through $C$.