The length of the common chord of two circles of radii 15 and 20, whose centres are 25 units apart, is 

Let $C_1$ and $C_2$ be the centers of the two circles of radii $r$ and $R$ respectively. Then

$C_1{C}_2=25,r=15$ and $R=20$               [Given]

We observe that $C_1{C}_2^2=r^2+R^2$

Thus, the two circles, intersect orthogonally.

$\therefore$Length of the common chord $=\frac{2rR}{\sqrt{r^2+R^2}}=\frac{2\times 15\times 20}{25}=24$