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P and Q are two points on the circle making the right angle at the center. The area of triangle POQ is 1568 sq. m, where O is the center of the circle. find the area of the minor segment?

P and Q are two points on the circle making the right angle at the center. The area of triangle POQ is 1568 sq. m, where O is the center of the circle. find the area of the minor segment? Correct Answer 896 sq. m

From the given information the diagram can be drawn as 

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∵ Δ POQ is a right angled triangle

∴ Area of the triangle POQ = 1568 sq m

1568 = 1 / 2 × base × height

1568 = 1 / 2 × r × r

r2 = 3136

Area of the minor sector = (θ / 360) × π r2

= 90/360 × 22/7 × 3136

= 2464 sq m

Area of minor segment (shaded area) = Area of the minor sector – Area of the triangle POQ

= 2464 - 1568

= 896 sq m

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