AHSME 1995 Problem 26

In the figure, $\overline{AB}$ and $\overline{CD}$ are diameters of the circle with center $O$, $\overline{AB} \perp \overline{CD}$, and chord $\overline{DF}$ intersects $\overline{AB}$ at $E$. If $DE = 6$ and $EF = 2$, then the area of the circle is

$\mathrm{(A) \ 23 \pi } \mathrm{(B) \ \frac {47}{2} \pi } \mathrm{(C) \ 24 \pi } \mathrm{(D) \ \frac {49}{2} \pi } \mathrm{(E) \ 25 \pi }$