{"status": "success", "data": {"description_md": "Circles with centers $A$ and $B$ have radii $3$ and $8$, respectively. A common internal tangent intersects the circles at $C$ and $D$, respectively. Lines $AB$ and $CD$ intersect at $E$, and $AE=5$. What is $CD$?\n[[Image:2006_AMC12A-16.png|center]]\n\n$\\mathrm{(A)}\\ 13\\qquad\\mathrm{(B)}\\ \\frac{44}{3}\\qquad\\mathrm{(C)}\\ \\sqrt{221}\\qquad\\mathrm{(D)}\\ \\sqrt{255}\\qquad\\mathrm{(E)}\\ \\frac{55}{3}$", "description_html": "<p>Circles with centers  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  have radii  <span class=\"katex--inline\">3</span>  and  <span class=\"katex--inline\">8</span> , respectively. A common internal tangent intersects the circles at  <span class=\"katex--inline\">C</span>  and  <span class=\"katex--inline\">D</span> , respectively. Lines  <span class=\"katex--inline\">AB</span>  and  <span class=\"katex--inline\">CD</span>  intersect at  <span class=\"katex--inline\">E</span> , and  <span class=\"katex--inline\">AE=5</span> . What is  <span class=\"katex--inline\">CD</span> ?<br/>\n[[Image:2006_AMC12A-16.png|center]]</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 13\\qquad\\mathrm{(B)}\\ \\frac{44}{3}\\qquad\\mathrm{(C)}\\ \\sqrt{221}\\qquad\\mathrm{(D)}\\ \\sqrt{255}\\qquad\\mathrm{(E)}\\ \\frac{55}{3}</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": "2006 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10A_p24", "prev": "/problem/06_amc10A_p22"}}