Question
Draw a circle of radius $4\ cm. $ Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?
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Answer
$1.$Mark any point $C$ on the sheet. Now, by adjusting the compasses up to $4\ cm$ and by putting the pointer of compasses at point $C,$ turn the compasses slowly to draw the circle. It is the required circle of $4\ cm$ radius.
$2.$Take any two chords $\overline{\text{AB}}$ and $\overline{\text{AB}}$ in the circle.
$3.$Taking $A$ and $B$ as centres and with radius more than half of $\overline{\text{AB}}$, draw arcs on both sides of $AB,$ intersecting each other at $E, F.$ Join $EF$ which is the perpendicular bisector of $AB.$
$4.$Taking $C$ and $D$ as centres and with radius more than half of $\overline{\text{CD}}$, draw arcs on both sides of $CD,$ intersecting each other at $G, H.$ Join $GH$ which is the perpendicular bisector of $CD.$
Now, we will find that when $EF$ and $GH$ are extended, they meet at the centre of the circle i.e., point $O.$
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