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 p…

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 \(A B\) in the ratio \(3: 2\) is the point \(C\) \((\alpha, \beta)\), then the length of the line segment \(A C\) is

[JEE Main 2023, 10 Apr (Shift 2)]