4. (10 points) Place the six numbers $1,3,5,7,9,11$ into the circles in the figure (each circle should contain only one number), so that the sum of the three numbers on each side is 17. Then, the sum of the three numbers in the circles at the three vertices of the triangle is . $\qquad$
【Analysis】According to the problem, let the three numbers in the circles at the three vertices of the triangle be $A$, $B$, and $C$; the sum of the numbers on each side is $1+3+5+7+9+11+A+B+C=17 \times 3$, and then solve further.

【Solution】Solution: Let the three numbers in the circles at the three vertices of the triangle be $A$, $B$, and $C$; according to the problem, we have:
$$
\begin{aligned}
1+3+5+7+9+11+A+B+C & =17 \times 3, \\
36+A+B+C & =51, \\
A+B+C & =15 .
\end{aligned}
$$
$$
1+3+11=15,3+5+7=15,1+5+9=15 ;
$$

Also, because: $1+9+7=17,9+3+5=17,1+11+5=17$;
Therefore, the three numbers in the circles at the three vertices of the triangle are 1, 9, and 5;
Thus, the number between 1 and 9 is 7, the number between 9 and 5 is 3, and the number between 1 and 5 is 11;
From the above, we get:
Therefore, the sum of the three numbers in the circles at the three vertices of the triangle is 15.
The answer is: 15.