Finding the coordinates of the center of a circle is an important problem in geometry, which involves the definition and properties of a circle. A circle is a set of all points whose distance from a plane to a fixed point is equal to a fixed length. This fixed point is the center of the circle, and this fixed length is the radius.

First, we need to know the basic definition of a circle. A circle is a set of all points on a plane equidistant from a given point (center). This distance is called the radius. Therefore, to find the center of the circle, you only need to find the point with the same distance as all the points.

Secondly, we need to know how to calculate the distance between two points. On the two-dimensional plane, the distance between two points can be calculated by Euclidean distance formula, that is, d = sqrt ((x2-x 1) 2+(y2-y 1) 2), where (x1,y1) and (x2, y2.

Then, we can traverse all the points on the circle and calculate their distances to a given point (such as the origin). If all points are at the same distance, then this given point is the center of the circle. If there are some points with unequal distances, then these points are not points on the circle, and we can exclude them.

Finally, we need to verify whether the found point is really the center of the circle. We can calculate the distance from this point to any two points on the circle. If these two distances are equal, then this point is the center of the circle.

Generally speaking, finding the coordinates of the center of a circle requires understanding the definition and properties of a circle, mastering the calculation method of the distance between two points, and finding the center of the circle through traversal and verification. This is a problem involving geometric knowledge and logical thinking, which requires a certain mathematical foundation and problem-solving skills.