Circle

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 \(\mathrm{AB}\) in the ratio \(3: 2\) is the point C\((\alpha, \beta)\), then the length of the line segment \(\mathrm{AC}\) is :