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Points of a Line within a Circle

Source: 2015 amc 10b #12

February 26, 2015
AMC

Problem Statement

For how many integers xx is the point (x,−x)(x,-x) inside or on the circle of radius 1010 centered at (5,5)(5,5)? <spanclass=′latex−bold′>(A)</span>11<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>13<spanclass=′latex−bold′>(D)</span>14<spanclass=′latex−bold′>(E)</span>15<span class='latex-bold'>(A) </span> 11 \qquad<span class='latex-bold'>(B) </span> 12 \qquad<span class='latex-bold'>(C) </span> 13 \qquad<span class='latex-bold'>(D) </span> 14 \qquad<span class='latex-bold'>(E) </span> 15
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