Problem
2004 AMC 12A 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}?
![[asy] 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)); [/asy]](/static/aops/daef6f3ebe3e1fc6cfacd8611db1d6d449c8d2d4.png)
\text {(A) } \frac {2 + \sqrt5}{2} \qquad \text {(B) } \sqrt 5 \qquad \text {(C) } \sqrt 6 \qquad \text {(D) } \frac52 \qquad \text {(E) }5 - \sqrt5
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