Peter used to be a “problem child”, but a recent 1 with his mother changed his life. After his father's death, Peter's life became much more difficult. His mother had to2 and was often not at home.

    His mother looked after him as well as possible. But3 Peter still caused problems. He was not4in studying. His mother was very5 and didn't give up. In the end, she made a 6: to send him to a boys' boarding school.

    One day, Peter told his teacher he wanted to leave the school. The teacher said he must7 with his mother. Peter called his mother, but this phone call 8 his life. “My mother helped me to understand how much she had given me. ”

    Now Peter has really changed. He is now one of the 9students in his class. His mother's10helped him to feel good about himself.

已知，在△ABC中，∠BAC=90°，∠ABC=45°，点D为直线BC上一动点（点D不与点B，C重合）．以AD为边作正方形ADEF，连接CF

（1）如图1，当点D在线段BC上时．求证：CF+CD=BC；

（2）如图2，当点D在线段BC的延长线上时，其他条件不变，请直接写出CF，BC，CD三条线段之间的关系；

（3）如图3，当点D在线段BC的反向延长线上时，且点A，F分别在直线BC的两侧，其他条件不变；

①请直接写出CF，BC，CD三条线段之间的关系；

②若正方形ADEF的边长为2$\sqrt{2}$，对角线AE，DF相交于点O，连接OC．求OC的长度．