AMC 12 2004a Problem 18

Square $ABCD$ has side length $2$. A semicircle with diameter $\overline{AB}$ is constructed inside the square, and the tangent to the semicircle from $C$ intersects side $\overline{AD}$ at $E$. What is the length of $\overline{CE}$?

size(100);
defaultpen(fontsize(10));
pair A=(0,0), B=(2,0), C=(2,2), D=(0,2), E=(0,1/2);
draw(A--B--C--D--cycle);draw(C--E);
draw(Arc((1,0),1,0,180));
label("$A$",A,(-1,-1));
label("$B$",B,( 1,-1));
label("$C$",C,( 1, 1));
label("$D$",D,(-1, 1));
label("$E$",E,(-1, 0));

$\text {(A) } \frac {2 + \sqrt5}{2} \text {(B) } \sqrt 5 \text {(C) } \sqrt 6 \text {(D) } \frac52 \text {(E) }5 - \sqrt5$