If a,b and c also represent the sides of a triangle and a,b,c are in g.p then the complete set of `alpha^2 = (r^2 +r +1)/(r^2-r+1)`is

Options

A. `(a-b)(c-a),(a-b)(b-c),(b-c)(c-a)` are in A.P
B. b-c,c-a,a-b are in H.P
C. a+b,b+c,c+a are in H.P
D. `a^2,b^2,c^2` are in H.P

Explanation

To solve the problem step by step, we start with the given conditions and proceed logically.

### Step 1: Understand the Given Conditions
We know that \( a, b, c \) are the sides of a triangle and are in geometric progression (G.P.). This means we can express them in terms of a common ratio \( r \):
- Let \( a = k \)
- Let \( b = kr \)
- Let \( c = kr^2 \)