Question 22Square $ABCD$ 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 $\overline{CE}?$ $\dfrac{2 + \sqrt{5}}{2}$$\sqrt{5}$$\sqrt{6}$$\dfrac{5}{2}$$5 - \sqrt{5}$
