Let
![ABCDEF](/media/m/9/f/e/9fe205b534135e3a700ffb54d8b96cb0.png)
be a convex hexagon with
![AB = DE](/media/m/3/8/b/38bd8922cad1473ac9fd60e0ad6c2672.png)
,
![BC = EF](/media/m/4/8/4/484cc8f8cef3b7a6fc4f7f004d5d8222.png)
,
![CD = FA](/media/m/5/c/6/5c63ab380593f0ae101d7f00eff0ae8c.png)
, and
![\angle A - \angle D = \angle C - \angle F = \angle E - \angle B](/media/m/4/9/c/49ccbc6dc1cedf20c18a25405bd171e5.png)
. Prove that the diagonals
![AD](/media/m/6/9/6/69672822808d046d0e94ab2fa7f2dc80.png)
,
![BE](/media/m/e/e/2/ee25cd134664bc0c8d7fdbba81e54f90.png)
, and
![CF](/media/m/6/7/0/670c216bc8a05762a60542376587c5fc.png)
are concurrent.
%V0
Let $ABCDEF$ be a convex hexagon with $AB = DE$, $BC = EF$, $CD = FA$, and $\angle A - \angle D = \angle C - \angle F = \angle E - \angle B$. Prove that the diagonals $AD$, $BE$, and $CF$ are concurrent.