Let the point B be the reflection of the point $\mathrm{A}(2,3)$ with respect to the line $8 \mathrm{x}-6 \mathrm{y}-23=0$. Let $\Gamma_{\mathrm{A}}$ and $\Gamma_B$ be circles of radii 2 and 1 with centres $A$ and $B$ respectively. Let $T$ be a common tangent to the circles $\Gamma_A$ and $\Gamma_B$ such that both the circles are on the same side of $T$. If $C$ is the point of intersection of T and the line passing through A and B , then the length of the line segment AC is $\_\_\_\_$