{"status": "success", "data": {"description_md": "Let $S$ be the set of circles in the coordinate plane that are tangent to each of the three circles with equations $x^{2}+y^{2}=4$, $x^{2}+y^{2}=64$, and $(x-5)^{2}+y^{2}=3$. What is the sum of the areas of all circles in $S$?\n\n$\\textbf{(A)}~48\\pi\\qquad\\textbf{(B)}~68\\pi\\qquad\\textbf{(C)}~96\\pi\\qquad\\textbf{(D)}~102\\pi\\qquad\\textbf{(E)}~136\\pi\\qquad$", "description_html": "<p>Let  <span class=\"katex--inline\">S</span>  be the set of circles in the coordinate plane that are tangent to each of the three circles with equations  <span class=\"katex--inline\">x^{2}+y^{2}=4</span> ,  <span class=\"katex--inline\">x^{2}+y^{2}=64</span> , and  <span class=\"katex--inline\">(x-5)^{2}+y^{2}=3</span> . What is the sum of the areas of all circles in  <span class=\"katex--inline\">S</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}~48\\pi\\qquad\\textbf{(B)}~68\\pi\\qquad\\textbf{(C)}~96\\pi\\qquad\\textbf{(D)}~102\\pi\\qquad\\textbf{(E)}~136\\pi\\qquad</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2022 AMC 10B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p23", "prev": "/problem/22_amc10B_p21"}}