Make an auxiliary line AB to connect PO, extend the intersection AB to g, and EF to H.

P is the bisector of arc AB.

So angle PAB= angle PBA PA=PB (the nature of a circle)

PO is the middle vertical line of the bisector AB of the triangle PAB (it can be proved that PO=OA=OB Angle POA= Angle POB).

CD is the focus of PA and PB, so CD is the center line of triangle pa and Pb.

EF‖AB po hangs vertically and divides EF CD equally.

So HD=HC HE=HF.

So CE=DF