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

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Answer:

Let circle C1 be given.

We have to find its centre.

1) Take points P, Q, R on the circle.

2) Join PR and RQ.

We know that perpendicular bisector of a chord passes through the centre. So, we construct perpendicular bisectors of PR & RQ .

3) Take a compass. With point P as pointly end and R as pencil end of the compass, mark an arc above and below PR .

Do same with R as pointly end and P as pencil end of the compass.

4) Join the points intersected by the arcs.

The line joined is the perpendicular bisector of PR.

5) Take a compass. With point R as pointly end and Q as pencil end of the compass, mark an arc above and below RQ.

Do same with Q as pointly end and R as pencil end of the compass.

6) Join the points intersected by the arcs. The line joined is the perpendicular bisector of RQ.

7) The point where the two perpendicular bisectors intersect is the centre of the circle.

8) Mark it as point O.

Thus, O is the centre of the given circle.

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