题目

Even facts “forgotten” by people during a busy day may be retrieved if this is followed by a good night’s sleep. Researchers from the University of Chicago asked volunteers to remember simple words．Many found their memories letting them down towards the end of the day, but the following morning, those who had slept well could recall much more. Researchers, writing in the journal Nature, said the brain could “rescue” lost memories during the night. When the brain is first asked to remember something that memory is laid down in an “unstable” state, meaning that it is possible tha如图，已知在△ABC中，∠BAC为直角，AB=AC，D为AC上一点，CE⊥BD于E．（1）若BD平分∠ABC，求证CE=BD；（2）若D为AC上一动点，∠AED如何变化？若变化，求它的变化范围；若不变，求出它的度数，并说明理由．