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

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