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