Locating The Center Of A Circle: Methods And Equations For Coordinate Determination.

Center of Circle

The given point that is circle is equidistant from

The center of a circle is the point that is equidistant from all points on the circumference of the circle. It can also be thought of as the midpoint of the diameter of the circle. The center is denoted by the letter O and is usually described by its coordinates in the Cartesian plane (x, y).

To find the coordinates of the center of a circle, you need to know two points on the circumference of the circle. Let (x1, y1) and (x2, y2) be the coordinates of two points on the circumference of the circle. Then, the coordinates of the center of the circle are:

x = (x1 + x2)/2
y = (y1 + y2)/2

Alternatively, if you know the equation of the circle, which is in the form of (x-a)^2 + (y-b)^2 = r^2, where (a,b) are the coordinates of the center and r is the radius of the circle, then the center is simply (a,b).

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