First of all, the point E I drew is next to the BC side, not the other three sides of the quadrilateral. Since you are not on the map, if it is different from yours, just draw my map first and get familiar with it.

Answer: Connect E and F.

Because ∠ DAB+∠ DCB = 180.

So ∠ ABC+∠ ADC = 180, ∠DCF=∠DAB.

Because ∠BCE=∠DCF.

So ∠CEB+∠DCF=∠ABC, ∠BFD+∠DCF=∠ADC.

Because ABC+ADC =180.

So ∠ CEB+∠ DCF+∠ BFD+∠ DCF = ∠ CEB+∠ BFD+2 ∠ DCF =180.

Because ∠CEF+∠CFE=∠DCF, 2*∠PED=∠AED, 2*∠PFB=∠AFB.

So ∠ PEF+∠ PFE =1/2 * ∠ AED+1/2 * ∠ AFB+∠ CEF+∠ CFE =1/2 * (\

So ∠ EPF = 90.

So EP⊥FP