$20 \cdot 104$ Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Then the length of the common chord of the two circles is 
(A) $3 \sqrt{11}$.
(B) $\frac{65}{6}$.
(C) $4 \sqrt{6}$.
(D) 10 .
(E) None of the above results is correct.
(Tianjin, China Junior High School Mathematics Competition, 1984)
[Solution] As shown in the figure, let the centers of the two circles be $O, O_{1}$, and the intersection points of the two circles be $A, B$.

Connect $O_{1} A$. In $\triangle O O_{1} A$, $O A=13, O O_{1}=$ $12, O A=5$.
Then, by $5^{2}+12^{2}=13^{2}$, we know that $\angle A O_{1} O$ is a right angle.
Thus, the chord $A B$ passes through $O_{1}$, and $A B=10$.
Therefore, the answer is $(D)$.