Muhammad's Congruent circles

Two congruent circles $\Gamma_1$ and $\Gamma_2$ each have radius $213,$ and the center of $\Gamma_1$ lies on $\Gamma_2.$ Suppose $\Gamma_1$ 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 $CD$ .

This problem is posed by Muhammad A.