Question 4
Let $A B C D E F$ be a convex hexagon such that $\angle A=\angle C=\angle E$ and $\angle B=\angle D=\angle F$ and the (interior) angle bisectors of $\angle A, \angle C$, and $\angle E$ are concurrent.
Prove that the (interior) angle bisectors of $\angle B, \angle D$, and $\angle F$ must also be concurrent.
Note that $\angle A=\angle F A B$. The other interior angles of the hexagon are similarly described.
Prove that the (interior) angle bisectors of $\angle B, \angle D$, and $\angle F$ must also be concurrent.
Note that $\angle A=\angle F A B$. The other interior angles of the hexagon are similarly described.