Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect?

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Solution

Draw a circle with centre at O. We draw two chords AB and CD as shown in the figure.

(i) With A as centre and radius more than half of AB, draw arcs on both sides of AB.
(ii) With the same radius and B as centre, draw arcs cutting the arcs of step (i) at P and Q.
(iii) Join P and Q.
(vi) With C as centre and radius more than half of CD, draw arcs on both sides of CD.
(v) With the same radius and D as centre, draw arcs cutting the arcs of step (iv) at R and S.
(vi) Join R and S.
We draw the line segments of perpendicular bisector of AB and CD.
We see that the perpendicular bisector of AB and CD meet at O, the centre of the circle.

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