Solution: (1) let C(0, b), according to the meaning of the question, there is b/ 12=3/b, and the solution is b=6, so C(0, 6);

(2) According to the meaning of the question, if the symmetry point of point B on a straight line cd on ac is E, then E (-6,3); if CD and BE intersect at F, then F (-3/2,3/2), then the linear equation of CD is (Y-3/2)/E(-6-3/2) = (X).

(3) There is a point N on the plane, so that the quadrilateral with O, C, M and N as the vertices is a diamond, and the coordinates of the point N are (-3√ 10/5.6-9/5√ 10), (3/2, 3) and (3.6,-0) respectively.