{"status": "success", "data": {"description_md": "A circle with center $C$ is tangent to the positive $x$ and $y$-axes and externally tangent to the circle centered at $(3,0)$ with radius $1$. What is the sum of all possible radii of the circle with center $C$?\n\n$\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ 4 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 8 \\qquad \\textbf{(E)}\\ 9$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A circle with center  <span class=\"katex--inline\">C</span>  is tangent to the positive  <span class=\"katex--inline\">x</span>  and  <span class=\"katex--inline\">y</span> -axes and externally tangent to the circle centered at  <span class=\"katex--inline\">(3,0)</span>  with radius  <span class=\"katex--inline\">1</span> . What is the sum of all possible radii of the circle with center  <span class=\"katex--inline\">C</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ 4 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 8 \\qquad \\textbf{(E)}\\ 9</span> </p>&#10;<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": 3, "problem_name": "2009 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p17", "prev": "/problem/09_amc12A_p15"}}