Let |(z̄-i)/(2 z̄+i)|=1/3, z ∈ C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are at the points (0,0),…

Let $\displaystyle \left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}, \mathrm{z} \in \mathbb{C}$, be the equation of a circle with center at C . If the area of the triangle, whose vertices are at the points $\displaystyle (0,0), C$ and $\displaystyle (\alpha, 0)$ is $\displaystyle 11$ square units, then $\displaystyle \alpha^2$ equals: