Question 99
For a convex hexagon $ABCDEF$, the angles formed by any pair chosen from the $3$ diagonals $AD, BE, CF$ are $60^\circ$. Prove that the inequality
$$
AB + BC + CD + DE + EF + FA \ge AD + BE + CF
$$
must hold.
Here, we say that a polygon is convex if all of its interior angles are less than $180^\circ$. We also denote by $XY$ the length of the line segment $XY$.
$$
AB + BC + CD + DE + EF + FA \ge AD + BE + CF
$$
must hold.
Here, we say that a polygon is convex if all of its interior angles are less than $180^\circ$. We also denote by $XY$ the length of the line segment $XY$.