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Question

In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and BOD = 90. Find the area of shaded region. [Use π = 3.14]

(3 Marks)


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Solution

In right triangle ABC

BC2=AB2+AC2=72+242=49+576=625,BC2=625BC=25
(1 mark)

Now,COD+BOD=180o ( Linear pair angles )

COD=180o90o=90o
(1 mark)

Now, the area of the shaded region = Area of the sector having the central angle 360o90o – Area of triangle ABC

=270o360o×π(BC2)212×AB×AC=34×3.14(252)212×7×24=367.9784=283.97 cm2
(1 mark)

Hence, the area of the shaded region is 283.97 cm2


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