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Question

Fig. 15.17, shows a sector of a circle, centre O, containing an angle θ. Prove that area of the shaded region is r22(tanθπθ180)
973436_034a748f929e40c8b77f24a43d4bfe78.png

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Solution

Area of shaded region
=arOABarea of sector
In OAB,tanθ=ABOA=ABr
AB=rtanθ
Now, required area=12×OA×OBθ360°×πr2
=12×r×rtanθθ360°πr2
=r22[tanθπθ180°]

955037_973436_ans_063e4037810b4e4693e1d45be2fa2101.png

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