Circles with centers $A$ and $B$ have radii  3 and 8, respectively. A common internal tangent touches the circles at $C$ and $D$, as shown. Lines $AB$ and $CD$ intersect at $E$, and $AE = 5$. What is $CD$?

[asy]
unitsize(0.2cm);
pair A,B,C,D,E;
A=(0,0);
B=(18.3,0);
E=(5,0);
C=(1.8,-2.4);
D=(13.5,6.4);
draw(Circle(A,3),linewidth(0.7));
draw(Circle(B,8),linewidth(0.7));
draw(A--B,linewidth(0.7));
draw(C--D,linewidth(0.7));
label("$A$",A,W);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,NW);
label("$E$",E,S);
[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Circles with centers $A$ and $B$ have radii  3 and 8, respectively. A common internal tangent touches the circles at $C$ and $D$, as shown. Lines $AB$ and $CD$ intersect at $E$, and $AE = 5$. What is $CD$?

[asy]
unitsize(0.2cm);
pair A,B,C,D,E;
A=(0,0);
B=(18.3,0);
E=(5,0);
C=(1.8,-2.4);
D=(13.5,6.4);
draw(Circle(A,3),linewidth(0.7));
draw(Circle(B,8),linewidth(0.7));
draw(A--B,linewidth(0.7));
draw(C--D,linewidth(0.7));
label("$A$",A,W);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,NW);
label("$E$",E,S);
[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{44}{3}
Circles with centers $A$ and $B$ have radii  3 and 8, respectively. A common internal tangent touches the circles at $C$ and $D$, as shown. Lines $AB$ and $CD$ intersect at $E$, and $AE = 5$. What is $CD$?

[asy]
unitsize(0.2cm);
pair A,B,C,D,E;
A=(0,0);
B=(18.3,0);
E=(5,0);
C=(1.8,-2.4);
D=(13.5,6.4);
draw(Circle(A,3),linewidth(0.7));
draw(Circle(B,8),linewidth(0.7));
draw(A--B,linewidth(0.7));
draw(C--D,linewidth(0.7));
label("$A$",A,W);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,NW);
label("$E$",E,S);
[/asy]
train