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प्रश्न
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 the shaded region.
उत्तर
BC is the diameter of the circle passing through the centre O.
Now,
∆ABC is a right angles triangle, right angled at A. (Angle subtended by the diameter on the circumference of the circle is 90°)
In right ∆ABC,
BC2 = AB2 + AC2
= (7)2 + (24)2
= 49 + 576
= 625
∴ BC = 25 cm
Also,
∠COD + ∠BOD = 180° (Linear pair angles)
⇒∠COD = 180° − 90° = 90°
Now,
Area of the shaded region = Area of sector OCABDO − Area of ∆ABC
`= 270^@/360^@ xx pi((BC)/2)^2 - 1/2 xx AB xx AC` (∵ 360° - 90° = 270° )
`= 3/4 xx 3.14 xx (25/2)^2 - 1/2 xx 7 xx 24`
= 367.97 - 84
= 283.97 cm2 (Approx)
Hence the area of shaded region is approximately 283.97 cm2
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