题目

Are your children liked by their teachers? All parents want their children to impress their teachers and succeed in school．You can get your children to impress their teachers by following these easy steps．     31   Teachers are impressed by children coming to school prepared to learn. Make sure they have everything they need：pencils，textbooks，erasers and so on．    32     Teach them to ask teachers questions when they don’t understand something. Some children think teachers are bothered by questions，but most teachers are impressed when children take the initi如图1，在正方形ABCD中，E是AB上一点，F是AD延长线上一点，且DF=BE．容易证得：CE=CF；（1）在图1中，若G在AD上，且∠GCE=45°，试猜想GE、BE、GD三线段之间的关系，并证明你的结论；（2）在（1）的条件下，若以C为圆心，CD为半径作圆，试判断此圆与直线EG的位置关系，并说明理由；（3）运用（1）中解答所积累的经验和知识，完成下题：如图2，在直角梯形ABCD中，AD∥BC（BC＞AD），∠B=90°，AB=BC=12，E是AB上一点，且∠DCE=45°，BE=4，求DE的长．