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Turkey NMO 2010 1st Round - P11 (Algebra)

Source:

July 27, 2012
analytic geometrygraphing linesslopegeometryperpendicular bisector

Problem Statement

At most how many points with integer coordinates are there over a circle with center of (20,10)(\sqrt{20}, \sqrt{10}) in the xyxy-plane?
<spanclass=latexbold>(A)</span> 8<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 1<spanclass=latexbold>(E)</span> None <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 1 \qquad<span class='latex-bold'>(E)</span>\ \text{None}