Concept: The sides of an obtuse triangle should satisfy the condition that the sum of the square of two smaller sides should be less than the square of the largest side. If a,b,c are in AP than b=‌
a+c
2
If a,b,c are in GP than b=√ac Calculation: log‌a−log‌2‌b,log‌2‌b−log‌3‌c and log‌3‌c−log a are in AP log‌2‌b−log‌3‌c=‌
log‌3‌c−log‌a+log‌a−log‌2‌b
2
log‌
2b
3c
=‌
log‌
3c
2b
2
‌
4b2
9c2
=‌
3c
2b
2b=3c‌‌-⋅s....(1) ∵a,b,c are in GP ⇒b2=ac...(2) From equation 1 and 2 we get 9c=4a a:b:c=9:2:4 As we know that, for obtuse triangle the sum of the square of two smaller sides should be less than the square of the largest side. ⇒a2>b2+c2 So, a,b and c are the sides of an obtuse angle triangle.