Let $A$ be the point $(1, 2)$ and $B$ be any point on the curve $x ^ { 2 } + y ^ { 2 } = 16$. If the centre of the locus of the point $P$, which divides the line segment $AB$ in the ratio $3 : 2$ is the point $C( \alpha , \beta )$, then the length of the line segment $AC$ is\\
(1) $\frac { 3 \sqrt { 5 } } { 5 }$\\
(2) $\frac { 4 \sqrt { 5 } } { 5 }$\\
(3) $\frac { 2 \sqrt { 5 } } { 5 }$\\
(4) $\frac { 6 \sqrt { 5 } } { 5 }$