Coordinate Geometry: JEE Main 2023 Mathematics question

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 :