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Question

# A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. The ratio of the area of the triangle to that of the square is

A
3:1
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B
3:2
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C
33:2
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D
33:2
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Solution

## The correct option is C 3√3:2Area of triangle =√34a2 (where a is one side of the triangle)Radius R of the circle =a2tan30∘=a2×1√3=a2√3∴ Diameter of the circle =a√3∴ Diagonal of the square =a√3∴ Area of the inscribed square =12×(a√3)2=a26∴ Ratio of the area of the triangle to that of the square=√3a24:a26=3√3:2

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