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Source: 2017 AMC 12B #9

February 16, 2017
2017 AMC 12BAMC 12AMCgeometrycircles

Problem Statement

A circle has center (−10,−4) (-10,-4) and radius 1313. Another circle has center (3,9)(3,9) and radius 65\sqrt{65}. The line passing through the two points of intersection of the two circles has equation x+y=cx+y=c. What is cc?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 33<spanclass=′latex−bold′>(C)</span> 42<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 132<span class='latex-bold'>(A)</span> \text{ 3} \qquad <span class='latex-bold'>(B)</span> \text{ } 3 \sqrt{3} \qquad <span class='latex-bold'>(C)</span> \text{ } 4\sqrt{2} \qquad <span class='latex-bold'>(D)</span> \text{ 6} \qquad <span class='latex-bold'>(E)</span> \text{ }\frac{13}{2}
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