{"status": "success", "data": {"description_md": "In the $xy$-plane, a circle of radius $4$ with center on the positive $x$-axis is tangent to the $y$-axis at the origin, and a circle with radius $10$ with center on the positive $y$-axis is tangent to the $x$-axis at the origin. What is the slope of the line passing through the two points at which these circles intersect?\n\n$\\textbf{(A)}\\ \\dfrac{2}{7} \\qquad\\textbf{(B)}\\ \\dfrac{3}{7}  \\qquad\\textbf{(C)}\\ \\dfrac{2}{\\sqrt{29}}  \\qquad\\textbf{(D)}\\ \\dfrac{1}{\\sqrt{29}}  \\qquad\\textbf{(E)}\\ \\dfrac{2}{5}$\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>In the  <span class=\"katex--inline\">xy</span> -plane, a circle of radius  <span class=\"katex--inline\">4</span>  with center on the positive  <span class=\"katex--inline\">x</span> -axis is tangent to the  <span class=\"katex--inline\">y</span> -axis at the origin, and a circle with radius  <span class=\"katex--inline\">10</span>  with center on the positive  <span class=\"katex--inline\">y</span> -axis is tangent to the  <span class=\"katex--inline\">x</span> -axis at the origin. What is the slope of the line passing through the two points at which these circles intersect?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\dfrac{2}{7} \\qquad\\textbf{(B)}\\ \\dfrac{3}{7}  \\qquad\\textbf{(C)}\\ \\dfrac{2}{\\sqrt{29}}  \\qquad\\textbf{(D)}\\ \\dfrac{1}{\\sqrt{29}}  \\qquad\\textbf{(E)}\\ \\dfrac{2}{5}</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": 2, "problem_name": "2023 AMC 12B Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12B_p11", "prev": "/problem/23_amc12B_p09"}}