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Draw a circle of radius $ 4 \mathrm{~cm} $. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?
To do:
We have to construct the perpendicular bisectors of the given chords and find where they meet.
Solution:
Steps of construction:
(i) Let us draw a circle of radius $4\ cm$ and name its centre as $O$.
(ii) Now, let us draw any two chords on the circle and name the first chord as $\overline{AB}$ and the second chord as $\overline{CD}$ respectively.
(iii) Now, by taking the measure with the compasses greater than half of the length of $\overline{AB}$ let us draw two arcs from point $A$ and point $B$ above and below $\overline{AB}$ and point the intersections of arcs as $E$ and $F$ respectively.
(iv) similarly by taking the measure greater than half of the length of $\overline{CD}$ let us draw two arcs from point $C$ and point $D$ above and below the $\overline{CD}$ point the intersections of arcs as $G$ and $H$ respectively.
(v) Now, let us join the points $E$ and $F$ and points $G$ and $H$ respectively.
(vi) Therefore, $\overline{EF}$ and $\overline{GH}$ form the perpendicular bisectors of $\overline{AB}$ and $\overline{CD}$ respectively when both the bisectors are extended we can observe that they meet the centre $O$ of the circle.
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