# Moving along a Circle

Geometry Level 2

For point $$(x,y)$$ moving along the circle $$x^2+y^2=4$$, let $$a$$ and $$b$$ be the maximum and minimum values, respectively, of $\frac{1}{1+x^2}+\frac{1}{1+y^2}.$ What is the value of $$ab$$?

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