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
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