jmc

The triangle is equilateral, since the three sides are equal radii. The common chord is twice an altitude of the triangle. The area of the triangle is $\frac{10^2\sqrt{3}}{4}=25\sqrt{3}$ sq cm, so the altitude (length $h$ cm) has $\frac{10h}{2}=25\sqrt{3}$ or $h=5\sqrt{3}$. The chord is twice this or $\boxed{10\sqrt{3}}$ cm.