Let D be the foot of the internal angle bisector of the angle A of a triangle ABC. Let E be a point on side [AC] such that ∣CE∣=∣CD∣ and ∣AE∣=65; let F be a point on the ray [AB such that ∣DB∣=∣BF∣ and ∣AB∣<∣AF∣=85. What is ∣AD∣?<spanclass=′latex−bold′>(A)</span>105<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>415<spanclass=′latex−bold′>(D)</span>75<spanclass=′latex−bold′>(E)</span>None of above