Multiple choice

Let P be a point inside a triangle ABC with $\angle$ABC $=90^o$. Let $P_1$ and $P_2$ be the images of P under reflection in AB and BC respectively. The distance between the circumcentres of triangles ABC and $P_1PP_2$ is?

  1. $\displaystyle\frac{AB}{2}$
  2. $\displaystyle\frac{AP+BP+CP}{3}$
  3. $\displaystyle\frac{AC}{2}$
  4. $\displaystyle\frac{AB+BC+AC}{2}$
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