Question

In the given figure, O is centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

Solution

AC = 24 cm, AB = 7 cm

Since BC is the diameter of the circle,

$So, ∠ BAC = 90 ° In right ∆ BAC, {BC}^{2} = {AC}^{2} = {AB}^{2} \Rightarrow {BC}^{2} = 24^{2} + 7^{2} \Rightarrow {BC}^{2} = 625 \Rightarrow BC = 25 So, the radius of the circle = OC = 12.5 cm Area of the shaded region = Area of the circle - Area of ∆ BAC - Area of sector CD = {πr}^{2} - \frac{1}{2} x AB X AC - \frac{θ}{360} X {πr}^{2} = (\frac{22}{7} x 12.5 x 12.5) - (\frac{1}{2} x 7 x 24) - (\frac{90}{360} x \frac{22}{7} x 12.5 x 12.5) . . . . . . . . . . (∵ ∠ BOD = 90 ° \Rightarrow ∠ COD = 90 °) = 491.07 - 84 - 122.77 = 284.3 {cm}^{2} (approximately) Hence, the area of the shaded region is 284.3 {cm}^{2} approximately .$

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In the given figure, O is centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

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Areas Related To Circles

In the given figure, O is centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

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