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Question

A chord 10 cm long is drawn in a circle whose radius is 52 cm. Find area of both the segments.

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Solution

In OAB,
OA2+OB2=50+50=100
AB2=102=100
i.e., OA2+OB2=AB2 which satisfies the Pythagoras theorem. Therefor,e θ=90°
Area of minor segment=area of sector-Area of AOB
=θ360°×πr212×OA×OB
=90°360°×227×52×5212×52×52
=39.2925=14.29cm2
Area of major segment=area of circle-area of minor segment
=πr214.29=227×52×5214.29
=142.85cm2

955032_973424_ans_72f7faf316764dd0a20e0b35def0c6aa.png

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