It is known that O is the center of ⊙O, A and B are on the circle, OA⊥AP, OB⊥BP?
Proof: PA=PB, ∠APO=∠BPO?
The above is the "tangent length theorem", which is of course true. ?
But its inverse proposition is not valid, so it cannot be proved. I can only cite counterexamples. ?
Actually? There are countless points A and B that satisfy the condition that "O is the center of ⊙O, A and B are on the circle, PA=PB, ∠APO=∠BPO". ?
As can be seen from the figure, A 1 and B 1 are a pair of points that meet the conditions, and A2 and B2 are another pair of points. There are countless pairs of such points. ?
As long as any point m is taken on the part (diameter ⊙O) in the straight line OP, and the straight line L passes through ⊙O to connect OA, OB, PA and PB, there must be PA = Pb, ∠ Apo = ∠ BPO, obviously. (a and b in the picture)?
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