Question

A square circumscribes a circle and another square is inscribed in this circle with one vertex at the point of contact. The ratio of the areas of the circumscribed and inscribed squares is 

(a) 1 : 2 

(b) 2 : 1 

(c) 3 : 1 

(d) 4 : 1

Answer 1

(b) 2 : 1

Let each edge of square ABCD = x units 

Then, area of square ABCD = x² 

For square EFGH, diag. HF = x

⇒ Side of square EFGH = \(\frac{x}{\sqrt2}\)

∴ Area of square EFGH = (\(\frac{x}{\sqrt2}\))² = \(\frac{x^2}{2}\)

∴ Required ratio = x² : \(\frac{x^2}{2}\) = 2 : 1.