Question 66
A square $ABCD$ of side $1$ is inscribed in a circle $\gamma$. Construct the reflections of the arcs $\overparen{AB}$, $\overparen{BC}$, $\overparen{CD}$, $\overparen{DA}$ of $\gamma$ in the sides $AB$, $BC$, $CD$, $DA$ respectively. Let $L, M, N, O$ be the midpoints of the arcs so obtained; what is the area of $LMNO$?
(A) $\frac{\sqrt{2}}{4}$
(B) $\sqrt{2}-1$
(C) $1-\frac{\sqrt{2}}{2}$
(D) $\frac{1}{4}$
(E) $3-2 \sqrt{2}$.
(A) $\frac{\sqrt{2}}{4}$
(B) $\sqrt{2}-1$
(C) $1-\frac{\sqrt{2}}{2}$
(D) $\frac{1}{4}$
(E) $3-2 \sqrt{2}$.