Suppose \( a, b, c \) are in A.P. Let \( A, G \) be the arithmetic mean and geometric mean betwe...

Suppose \( a, b, c \) are in A.P. Let \( A, G \) be the arithmetic mean and geometric mean between \( a \) and \( b, A^{\prime}, G^{\prime} \) be the arithmetic mean and geometric mean between \( b \) and \( c \), then
(a) \( A^{2}+G^{2}=A^{\prime 2}+G^{\prime 2} \)
(b) \( A^{2}-G^{2}=A^{2}-G^{2} \)
(c) \( A^{2}-A^{2}=G^{2}-G^{2} \)
(d) \( A^{2}+A^{2}=G^{2}+G^{2} \)