Correct option (B) obtuse angled
We have 2(log2b − log3c) = loga − log2b + log3c − loga ⇒ 3(log2b − log3c) = 0 ⇒ 2b = 3c
Further, b2 = ac ⇒ 9c2 /4 = ac ⇒ c = 4a/9
Thus, a = 9c/4 and b = 3c/2 ⇒ a : b : c = 9/4 : 3/2 : 1 = 9 : 6 : 4
Clearly, sum of any two are greater than third, so they form a triangle.
Also, cos A = 42 + 62 - 92/2.4.6 = 29/48 ⇒ is obtuse angle.