Consider the following figure, with $|\text{AD}|=|\text{CE}|$.

If $|\text{AB}|=|\text{CB}|$, then $\text{AC}$ is parallell to $\text{DE}$ and $|\text{DE}|=\frac{|\text{AB}|}{|\text{AD}|}|\text{AC}|\le |AC|$, by the Intercept Theorem.
If we don't suppose anything, it seems true that we still always have $|\text{DE}|\le |\text{AC}|$. Does this result have a name ? How might it be proved ?
