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 $C$.
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