In the accompanying figure $ \overline{CE}$ and $ \overline{DE}$ are equal chords of a circle with center $ O$. Arc $ AB$ is a quarter-circle. Then the ratio of the area of triangle $ CED$ to the area of triangle $ AOB$ is:
[asy]defaultpen(linewidth(.8pt));
unitsize(2cm);

pair O = origin;
pair C = (-1,0);
pair D = (1,0);
pair E = (0,1);
pair A = dir(-135);
pair B = dir(-60);

draw(Circle(O,1));
draw(C--E--D--cycle);
draw(A--O--B--cycle);

label("$A$",A,SW);
label("$C$",C,W);
label("$E$",E,N);
label("$D$",D,NE);
label("$B$",B,SE);
label("$O$",O,N);[/asy]
$ \textbf{(A)}\ \sqrt {2} : 1\qquad \textbf{(B)}\ \sqrt {3} : 1\qquad \textbf{(C)}\ 4 : 1\qquad \textbf{(D)}\ 3 : 1\qquad \textbf{(E)}\ 2 : 1$
1. **Determine the area of triangle \( \triangle AOB \):**
   - Since arc \( AB \) is a quarter-circle, the central angle \( \angle AOB \) is \( 90^\circ \).
   - Let the radius of the circle be \( r \).
   - The area of \( \triangle AOB \) can be calculated using the formula for the area of a right triangle:
     \[
     \text{Area of } \triangle AOB = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times r \times r = \frac{r^2}{2}
     \]

2. **Determine the area of triangle \( \triangle CED \):**
   - Chords \( \overline{CE} \) and \( \overline{DE} \) are equal, and \( \overline{CD} \) is the diameter of the circle.
   - Since \( \overline{CD} \) is the diameter, \( \angle CED \) is a right angle (\( 90^\circ \)) by the Inscribed Angle Theorem.
   - The length of \( \overline{CD} \) is \( 2r \) (the diameter of the circle).
   - The height of \( \triangle CED \) from \( E \) to \( \overline{CD} \) is \( r \) (the radius of the circle).
   - The area of \( \triangle CED \) can be calculated using the formula for the area of a right triangle:
     \[
     \text{Area of } \triangle CED = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2r \times r = r^2
     \]

3. **Calculate the ratio of the areas:**
   - The area of \( \triangle CED \) is \( r^2 \).
   - The area of \( \triangle AOB \) is \( \frac{r^2}{2} \).
   - The ratio of the area of \( \triangle CED \) to the area of \( \triangle AOB \) is:
     \[
     \frac{\text{Area of } \triangle CED}{\text{Area of } \triangle AOB} = \frac{r^2}{\frac{r^2}{2}} = \frac{r^2 \times 2}{r^2} = 2
     \]

The final answer is \(\boxed{2:1}\).