MathNet 2026 — Part 10 Question 135

In convex hexagon $A B C D E F$, $\angle A = \angle B$, $\angle C = \angle D$, and $\angle E = \angle F$. Prove that the perpendicular bisectors of $\overline{A B}$, $\overline{C D}$, and $\overline{E F}$ pass through a common point.