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You, of course, "brilliantly" set the task.
But suppose that you simply did not think that there might be something incomprehensible in your formulation of the question.
If we are talking about a circle on a plane in Cartesian coordinates, then the radius will not be enough for you to calculate the coordinates of the center of the circle.
It will require, at a minimum, either a point on the border of the circle and a direction (for example, a normal vector), then the center will be calculated by the vector difference of the coordinates of the point and the product of the normal and the radius.
You can find the center by the radius and two points on the border of the circle. What are the inputs?
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