{"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 $CD$?

[asy] unitsize(2.5mm); defaultpen(fontsize(10pt)+linewidth(.8pt)); dotfactor=3; pair A=(0,0), Ep=(5,0), B=(5+40/3,0); pair M=midpoint(A--Ep); pair C=intersectionpoints(Circle(M,2.5),Circle(A,3))[1]; pair D=B+8*dir(180+degrees(C)); dot(A); dot(C); dot(B); dot(D); draw(C--D); draw(A--B); draw(Circle(A,3)); draw(Circle(B,8)); label(\"$A$\",A,W); label(\"$B$\",B,E); label(\"$C$\",C,SE); label(\"$E$\",Ep,SSE); label(\"$D$\",D,NW); [/asy]
\n\n$\\mathrm{(A)}\\ 13\\qquad\\mathrm{(B)}\\ \\frac{44}{3}\\qquad\\mathrm{(C)}\\ \\sqrt{221}\\qquad\\mathrm{(D)}\\ \\sqrt{255}\\qquad\\mathrm{(E)}\\ \\frac{55}{3}$\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": "

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 ?

\"[asy]

\\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}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2006 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12A_p17", "prev": "/problem/06_amc12A_p15"}}