题目

School violence is in the headlines again after recent shootings at schools in Pennsylvania, Wisconsin, and Colorado. After hearing the news, it’s natural for students — no matter how old they are or where they go to school — to worry about whether this type of incident may someday happen to them.     So how safe are schools? It’s actually safer to be in a school than in a car. Twice as many 15-to-19-year-olds die in car accidents than in shootings (and that’s all shootings, not just the ones that happen in schools). According to the Centers for Disease Control and Prevention, les已知△ABC中，BC=6，AC＞AB，点D为AC边上一点，且DC=AB=4，E为BC边的中点，连接DE，设AD=x．（1）当DE⊥BC时（如图1），连接BD，则BD的长为______；（2）设，求y关于x的函数关系式，并写出x的取值范围；（3）取AD的中点M，连接EM并延长交BA的延长线于点P，以A为圆心AM为半径作⊙A，试问：当AD的长改变时，点P与⊙A的位置关系变化吗？若不变化，请说明具体的位置关系，并证明你的结论；若变化，请说明理由．