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Let us call the point where the excircle touches PQ, as D. 

   PD = PB   as these lengths of tangents from P to a circle.
  QD = QC    same reason.

   PQ = PD + DQ = PB + QC
Perimeter = AP + PQ + AQ
               = AP + PB + QC + AQ
             = AB + AC
               = 9 cm + 9 cm  = 18 cm

      AC = AB as these are tangents from the same point A to the circle.

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