Square ABCD is inscribed in a circle, and P is a point on arc BC of the circle.
By applying Ptolemy's Theorem to cyclic quadrilaterals PBAD and PADC respectively we have:
PA×BD=PB×AD+PD×AB=AB(PB+PD)
PD×AC=PC×AD+PA×CD=AB(PA+PC)
Now by dividing these two we get,
PA+PCPB+PD = PDPA