Consider a right angled triangle $\triangle A B C$ whose hypotenuse $A C$ is of length 1. The bisector of $\angle A C B$ intersects $A B$ at $D$. If $B C$ is of length $x$, then what is the length of $CD$?\\
(A) $\sqrt { \frac { 2 x ^ { 2 } } { 1 + x } }$\\
(B) $\frac { 1 } { \sqrt { 2 + 2 x } }$\\
(C) $\sqrt { \frac { x } { 1 + x } }$\\
(D) $\frac { x } { \sqrt { 1 - x ^ { 2 } } }$