题目

A student was one day taking a walk with his teacher. As they went along, they saw a pair of old shoes lying in the path. They were a poor farmer’s, who was working in the nearby field.         The student turned to the teacher, saying: “we will hide his shoes, and hide ourselves behind those trees, and wait to see what he will do.”      “My young friend,” answered the teacher, “we should never make fun of the poor. Why not put a coin in each shoe, and then we will hide ourselves and watch?” The student did so and they both hid themselves behind the trees. 如图，在△ABC中，AB=AC，点D是△ABC内一点，AD=BD，且AD⊥BD，连接CD．过点C作CE⊥BC交AD的延长线于点 E，连接BE．过点D作DF⊥CD交BC于点F．（1）若BD=DE=，CE=，求BC的长； （2）若BD=DE，求证：BF=CF．