If so, the answer is:

Certificate:

Because AD is the bisector of angle BAC.

So angle EAD= angle FAD

Angle AED= angle AFD = 90.

AD=AD

So triangle AED= triangle AFD

So AE=AF.

So triangle EAF is an isosceles triangle.

Because AD is an angular bisector,

So AD is perpendicular to EF (the bisector of isosceles triangle bisects the base vertically).