Monotonicity of a length in a figure Here is something I have been wondering about today... It seems graphically obvious, but I haven't been able to find a "clean" proof of it.

If $x_1>x_2$, then $d_1>d_2$ in the following figure:


Would someone have a clue ?

As $BC=BD$ the perpendicular bisector $m$ of $CD$ goes through $B$. The assumption $x_1>x_2$ means that the point $A$ is to the right of $m$, and the same is then true for the point $E$. It follows that $d_1>d_2$.
