Circle

Let the point B be the reflection of the point A(2,3) with respect to the line 8x−6y−23=0.Let CA and CB be circles of radii 2 and 1 with centers A and B respectively. Let T be a common tangent to the circles CA and CB such that both the circles are on the same side of T. If C is the point of intersection of C and the line passing through A and B, then the length of the line segment AC is ______