Traditional Culture Encyclopedia - Photography and portraiture - (junior high school olympiad) It is known that P is a point outside the circle O, PA and PB are two tangents of the circle O, PE is the secant of the circle, and the circle O intersects with C and E.

(junior high school olympiad) It is known that P is a point outside the circle O, PA and PB are two tangents of the circle O, PE is the secant of the circle, and the circle O intersects with C and E.

Connect PO and AB to h, then AB⊥PO,

Based on the projective theorem of right triangle,

PO×PH=PA^2，

And because pa 2 = PC × PE,

So PC x PE = ph x po,

So EOHC is a four-point circle,

So ∠EHO =∠ economy =∠OEC=∠CHP.

So HB is the angular bisector of ∠EHC,

∠DHP =90 again? ,

So HP is the bisector of the outer corner of ∠EHC.

Base on that bisector theorem of the inner and out angles of a triangle,

Know that ED/CD=EH/HC=EP/PC

That is ED/CD=EP/PC,

∴PE×CD=PC×DE