MathDB

Let

ABCDEF

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 FAB

. The other interior angles of the hexagon are similarly described.

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