[ Similar triangles (other).]

Three lines, parallel to the sides of a given triangle, cut off three triangles from it, and a regular hexagon remains.

Find the length of the side of the hexagon if the lengths of the sides of the triangle are $a, b$, and $c$.
Let the side of the hexagon be $x$. From the consideration of similar triangles, we obtain the equality ${ }^{a x} /{ }_{c}+x$ $+a x / b=a$.

Answer

$a b c / a b+b c+a c$.