(2) Maximize the area and fix the length of AB side, that is, the distance from C to AB side is the largest. For this kind of problem, the usual solution is to make a vertical line through the center of the circle, and then the maximum and minimum distance is plus or minus the radius. But this problem only requires the maximum value, and the slope of straight line AB is-1, so the slope of vertical line passing through point O is 60.
(3)∵OC⊥OD, and oc∨ad, then there must be OD⊥AD, that is to say, AD is the tangent of circle O. If point D is below the X axis, it is obviously irrelevant.
Point A rotates 90 counterclockwise around the central point O, just to point B, and point D also rotates 90 counterclockwise around the central point O, and to point C, AD is the tangent of circle O, so BC is also the tangent of circle O.
That is to say, △BOC is a right triangle, and Pythagorean theorem finds that the length of BC is 3√3.
The distance between C and Y axis is 3√3/2, and the distance between C and X axis is 3/2.
∴C(-3√3/2,3/2)