User:Jonjoseph
![[asy] pair O = (0,0); pair P = (2,0); draw(unitcircle); dot(O); dot(P); label('$P$', P, E); label('$C$', O, W); [/asy]](http://latex.artofproblemsolving.com/f/8/c/f8c42e0581ece077163a0525688493127ba20734.png)
Given a circle with center 
and a point 
that lies outside the circle, bisect circle with a second circle centered at .
![[asy] pair O = (0,0); pair P = (2,0); pair A = (0,1); pair B = (0, -1); draw(unitcircle); draw(A--B, red); draw(P--O, red); draw(circle(P, 2.24)); dot(O); dot(P); dot(A); dot(B); label('$P$', P, E); label('$C$', O, W); [/asy]](http://latex.artofproblemsolving.com/e/b/4/eb4535e9b70c84a691a32b89d485892fe6de6140.png)
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