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

**Answer Choices**

A. \dfrac{2+\sqrt{5}}{2}

B. \sqrt{5}

C. \sqrt{6}

D. \dfrac{5}{2}

E. 5 \quad \sqrt{5}