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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.
Solution
In right triangle ABC
BC2 = AB2 + AC2
= (7)2 + (24)2
= 49 + 576
= 625
∴ BC2 = 625
⇒ BC = 25
Now, ∠COD + ∠BOD = 180° (Linear pair angles)
⇒∠COD = 180° − 90° = 90°
Now, Area of the shaded region = Area of sector having central angle (360° − 90°) − Area of triangle ABC
`=270^circ/360^circpi(BC)^2 - 1/2"AB" × "AC"`
`= 3/4xx3.14xxx(25/2)^2 - 1/2xx7xx24`
= 367.97 × 84
= 283.97 cm2
Hence, the area of shaded region is 283.97 cm2
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