As shown in the figure, square ABCD is inscribed in ⊙ o, q is a moving point on diameter AC, connecting DQ and extending intersection ⊙ o to P. if QP = Qo, then the value of QAQC is______ ．

Let the radius of ⊙ o be r, Qo = m, then QP = m, QC = R + m, QA = r-m. in ⊙ o, according to the intersecting chord theorem, we get QA ⊙ QC = QP ⊙ QD. That is, (R-M) (R + m) = m ⊙ QD, so QD = R2 − M2M

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