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 :

Question

$\frac{3 \sqrt{5}}{5}$

$\frac{6 \sqrt{5}}{5}$

$\frac{2 \sqrt{5}}{5}$

$\frac{4 \sqrt{5}}{5}$

Solution

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