The logs are in AP:

\(2(\log 2b - \log 3c) = (\log a - \log 2b) + (\log 3c - \log a) = \log 3c - \log 2b\)

\(3\log 2b = 3\log 3c \Rightarrow 2b = 3c \Rightarrow b = \frac{3c}{2}\)

From the GP, \(b^2 = ac\): \(\frac{9c^2}{4} = ac \Rightarrow a = \frac{9c}{4}\).

So the sides are in the ratio \(a : b : c = 9 : 6 : 4\). Largest side squared: \(81 > 36 + 16 = 52\).

So the triangle is obtuse-angled.

Answer: (B)