Question

Suppose you are given a circle. Give a construction to find its centre.

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Answer 1

Answer:

circle.

Steps of construction:

Steps of construction:1. Taking three points P, Q and R on the circle.

Steps of construction:1. Taking three points P, Q and R on the circle.2. Join PQ and QR.

Steps of construction:1. Taking three points P, Q and R on the circle.2. Join PQ and QR.3. Draw MQ and NS, respectively the perpendicular bisectors of PQ and RQ, which intersect each other at O.

Steps of construction:1. Taking three points P, Q and R on the circle.2. Join PQ and QR.3. Draw MQ and NS, respectively the perpendicular bisectors of PQ and RQ, which intersect each other at O.Hence, O is the centre of the circle.

Answer 2

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${(i)}$ Take any three points P, Q and R on the circle.

${(ii)}$ Join PQ and QR.

${(iii)}$ Draw the perpendicular bisectors of PQ and QR. Let these intersect at O.

Then, O is the centre of the circle.

And we are done! :D

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