Q4 of 805 Page 17

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?

Steps of construction:


(i) Draw a circle with centre O.


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(ii) Draw its two chords AB and CD such that AB is not parallel to CD.


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(iii) Draw a circle with centre A with radius more than 1/2 AB.


Similarly, Draw a circle with centre B with same radius which intersect above circle at M and N respectively.


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(iv) Draw line segment MN which intersect AB at point P.


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(v) Similarly, Draw a circle with centre C with radius more than 1/2 CD.


Similarly, Draw a circle with centre D with same radius which intersect above circle at X and Y respectively.


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(vi) Draw line segment XY which intersect CD at point Q.


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We can see that two bisectors MN and XY intersects at centre O.


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