Original title of mathematics finale in Shenzhen senior high school entrance examination
25. as shown in figure 1, in ⊙O, AB is the diameter, c is the point above ⊙O, ∠ ABC = 45, in the isosceles right triangle DCE, ∠ is the right angle, and point D is on the line segment AC.
(1) Proof: three-point * * * lines of B, C and E;
(2) If M is the midpoint of line segment BE and N is the midpoint of line segment AD, it is proved that MN=
2OM
(3) Rotate △DCE counterclockwise around point C by α(0