If \( a, b \), and \( c \) are in A.P., and \( p \) and \( p^{\prime} \) are, respectively, A.M....

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If \( a, b \), and \( c \) are in A.P., and \( p \) and \( p^{\prime} \) are, respectively, A.M. and G.M. between \( a \) and \( b \) while \( q, q^{\prime} \) are, respectively, the A.M. and G.M. between \( b \) and \( c \), then
(A) \( p^{2}+q^{2}=p^{2}+q^{\prime 2} \)
(B) \( p^{2}-q^{2}=p^{2}-q^{2} \)
(C) \( p q=p^{\prime} q^{\prime} \)
(D) none of these
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