9. 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 conclusions is correct.
Answer $(\quad)$
9. (D)

Let the angle between the radius of the larger circle (from the intersection point to the center) and the line connecting the centers be $\alpha$. Clearly, $\alpha<90^{\circ}$, thus
$$
\cos \alpha=\frac{13^{2}+12^{2}-5^{2}}{2 \cdot 12 \cdot 13}=\frac{12}{13}, \quad \sin \alpha=\frac{5}{13},
$$

Therefore, the length of the common chord is $2 \cdot 13 \cdot \sin \alpha=2 \cdot 13 \cdot \frac{5}{13}=10$.