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SMO 2005 Senior Round 1 Question 10

SMO · SMO 2005 Senior Round 1

Question 10

Let $x,y$ be real numbers such that
$$x^2+y^2=2x-2y+2.$$
What is the largest possible value of $x^2+y^2$?
  1. $10+8\sqrt2$
  2. $8+6\sqrt2$
  3. $6+4\sqrt2$
  4. $4+2\sqrt2$
  5. None of the above