Inscribed Angles on a Diameter

Congruent circles $\Gamma_1$ and $\Gamma_2$ have radius $2012,$ and the center of $\Gamma_1$ lies on $\Gamma_2.$ Suppose that $\Gamma_1$ and $\Gamma_2$ intersect at $A$ and $B$. The line through $A$ perpendicular to $AB$ meets $\Gamma_1$ and $\Gamma_2$ again at $C$ and $D$, respectively. Find the length of $CD$.

Source: 2011-2012 Winter Online Math Open