Let the point B be the reflection of the point A(2, 3) with respect to the line 8x − 6y − 23 = 0. Let Γₐ and Γᵦ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles Γₐ and Γᵦ 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 _____.