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Gaokao Math Practice Question

已知圆 $O$ 的半径为 $1, P A$、 $P B$ 为该圆的两条切线, $A$、 $B$ 为两切点, 那么 $\overrightarrow{\mathrm{PA}} \cdot \overrightarrow{\mathrm{PB}}$ 的最小值为 ($\qquad$)

  1. A.$-4+\sqrt{2}$
  2. B.$-3+\sqrt{2}$
  3. C.$-4+2 \sqrt{2}$
  4. D.$-3+2 \sqrt{2}$

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