Let a pointP inside a parallelogram ABCD be given such that <APB +<CPD = 180◦.

Prove that

AB· AD = BP · DP + AP · CP

(here AB, AD etc. refer to the lengths of the corresponding segments).

I think that P could be in the very centre, but am unsure how to go about the question, and initially unsure about a possible position for 'p'.

Help would be great