Question 48
A circle with centre $O$ is inscribed in a square with side length $a$. Four smaller circles with centres $O_{1}$, $O_{2}$, $O_{3}$ and $O_{4}$ touch the larger circle and two sides of the square each (see the figure). What is the area of the square $O_{1} O_{2} O_{3} O_{4}$?
(A) $3 a^{2}(3-2 \sqrt{2})$
(B) $4 a^{2}(3-2 \sqrt{2})$
(C) $a^{2}(3-\sqrt{2})$
(D) $a^{2}(2-\sqrt{2})$
(E) $3 a^{2}(2-\sqrt{2})$
(A) $3 a^{2}(3-2 \sqrt{2})$
(B) $4 a^{2}(3-2 \sqrt{2})$
(C) $a^{2}(3-\sqrt{2})$
(D) $a^{2}(2-\sqrt{2})$
(E) $3 a^{2}(2-\sqrt{2})$