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?

Answer 1

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"AB"` and `overline"CD"` in the circle.
   
3. Taking A and B as centres and with radius more than half of `overline"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"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.