It is known that in △ ABC, ab = AC, BD = DC, AE bisects ∠ fac, try to guess the position relationship between AE and ad, please explain the reason

It is known that in △ ABC, ab = AC, BD = DC, AE bisects ∠ fac, try to guess the position relationship between AE and ad, please explain the reason

Vertical relationship
According to the chart, the title should be AE equal ∠ fab
The triangle ABC is an isosceles triangle with three lines in one,
Ad is the center line, and it is also the angular bisector, so ∠ DAB = 1 / 2 ∠ cab, and ∠ BAE = 1 / 2
Therefore, ead = 1 / 2 (∠ cab + ∠ FAB) = 90