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An equilateral triangle ABC is inscribed in a circle as shown in figure. A square of largest possible area is made inside this triangle as shown. What is the ratio of area of large circle and the small circle?

An equilateral triangle ABC is inscribed in a circle as shown in figure. A square of largest possible area is made inside this triangle as shown. What is the ratio of area of large circle and the small circle? Correct Answer 4(7 + 4√3) : 9

Diameter of the small circle = Side of the square

Radius of the small circle = 1/2 × s = AB/2 × (2√3 - 3) cm

(Radius of large circle)/(Radius of small circle) = (AB/√3)/

⇒ 2(2 + √3)/3

Ratio of area = (Ratio of radii)2

Required ratio = (2(2 + √3)/3)2 = 4(7 + 4√3)/9

∴ Ratio of the area of the large circle to small circle = 4(7 + 4√3) : 9

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