Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
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 the inscribed squares is
(a)1
(b)2 : 1
(c)3
(d)4
Answer
Answer (as printed): A
Explanation
Let the radius of the circle be $r$ and the side of the circumscribed and inscribed squares be $a_{1}$ and $a_{2}$ respectively. Then, $a_{1}=2 r$. Diagonal of inscribed square $$\begin{aligned} & =2 r \Rightarrow \sqrt{2} a_{2}=2 r \Rightarrow a_{2}=\frac{2 r}{\sqrt{2}}=\sqrt{2} r . \\ & \therefore \quad \text { Required ratio }=\frac{a_{1}^{2}}{a_{2}^{2}}=\frac{(2 r)^{2}}{(\sqrt{2} r)^{2}}=\frac{4 r^{2}}{2 r^{2}}=2: 1 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.