Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the length of CE?[asy]defaultpen(linewidth(0.8));
pair A=origin, B=(1,0), C=(1,1), D=(0,1), X=tangent(C, (0.5,0), 0.5, 1), F=C+2*dir(C--X), E=intersectionpoint(C--F, A--D);
draw(C--D--A--B--C--E);
draw(Arc((0.5,0), 0.5, 0, 180));
pair point=(0.5,0.5);
label("A", A, dir(point--A));
label("B", B, dir(point--B));
label("C", C, dir(point--C));
label("D", D, dir(point--D));
label("E", E, dir(point--E));[/asy]<spanclass=′latex−bold′>(A)</span>22+5<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>25<spanclass=′latex−bold′>(E)</span>5−5