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

As angles `A,B and C` are in A.P.

`:. 2B = A+C`

Now, `A+B+C = 180 => B+2B+ 180`

`=>3B = 180 =>B= 60^@`

Now, `cos B = (a^2+c^2 - b^2)/(2ac)`

`=>cos 60^@ = (a^2+c^2 - b^2)/(2ac)`

`=>1/2 = (a^2+c^2 - b^2)/(2ac)`

`=>ac = a^2+c^2 - b^2->(1)`

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