Given an arc of a circle, complete the circle.

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Solution

Let PQ be an arc of the circle.

In order to complete the circle. First of all we have to find out its centre and radius.

Now take a point R on the arc PQ and join PR and QR.

Draw the perpendicular bisectors of PR and QR respectively.

Let these perpendicular bisectors intersect at point O.

Then OP = OQ, draw a circle with centre O and radius OP = OQ to get the required circle.

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\frac{θ}{360^{\circ}} \times 2 π r^{2} .

r a d i u s o f c i r c l e = 20 c m, l e n g t h o f a r c = 78.50 c m (π = 3.14)

θ

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40^{\circ}

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