Let ABCD be a square of side of unit length. Let a circle C_1 centered at A with unit radius is drawn. Another circle C_2 which touches C_1 and the…

Let ABCD be a square of side of unit length. Let a circle $\displaystyle \mathrm{C}_1$ centered at A with unit radius is drawn. Another circle $\displaystyle \mathrm{C}_2$ which touches $\displaystyle \mathrm{C}_1$ and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle $\displaystyle \mathrm{C}_2$ meet the side AB at E . If the length of EB is $\displaystyle \alpha+\sqrt{3} \beta$, where $\displaystyle \alpha, \beta$ are integers, then $\displaystyle \alpha+\beta$ is equal to \_\_\_\_.