If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that `a^2, b^2,c^2` are in A.P.

Explanation

To prove that \( a^2, b^2, c^2 \) are in A.P. given that the angles \( A, B, C \) of a triangle are in A.P. and the sides \( a, b, c \) are in G.P., we can follow these steps:

### Step 1: Understand the conditions
Given that the angles \( A, B, C \) are in A.P., we can express this as:
\[ 2B = A + C \]
Also, since the sum of angles in a triangle is \( 180^\circ \):
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