Current location - Training Enrollment Network - Mathematics courses - Original title of mathematics finale in Shenzhen senior high school entrance examination
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