Question

# A circle is inscribed in an equilateral triangle of side a, the area of any square inscribed in the circle is

Solution

## The correct option is C If p be the altitude, then p = asin 60∘ = a2√3. Since the triangle is equilateral, therefore centroid, orthocentre, circumcentre and incentre all coincide. Hence, radius of the inscribed circle = 13p=a2√3=r or diameter=2r=a√3. Now if x be the side of the square inscribed, then angle in a semicircle being a right angle, hence x2+x2=d2=4r2⇒2x2=a23 So the area of the square is x2=a26

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