# Problem #2114

 2114 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 $\overline{CE}$? $[asy] size(100); defaultpen(fontsize(10)); pair A=(0,0), B=(2,0), C=(2,2), D=(0,2), E=(0,1/2); draw(A--B--C--D--cycle);draw(C--E); draw(Arc((1,0),1,0,180)); label("A",A,(-1,-1)); label("B",B,( 1,-1)); label("C",C,( 1, 1)); label("D",D,(-1, 1)); label("E",E,(-1, 0)); [/asy]$ $\text {(A)} \frac {2 + \sqrt5}{2} \qquad \text {(B)} \sqrt 5 \qquad \text {(C)} \sqrt 6 \qquad \text {(D)} \frac52 \qquad \text {(E)}5 - \sqrt5$ This problem is copyrighted by the American Mathematics Competitions.
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