Problem 9.6. Given an obtuse triangle $ABC$ with an obtuse angle $C$. On its sides $AB$ and $BC$, points $P$ and $Q$ are marked such that $\angle ACP = CPQ = 90^\circ$. Find the length of the segment $PQ$, if it is known that $AC = 25, CP = 20, \angle APC = \angle A + \angle B$.

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