## center of a circle

### The center of a circle is a point that is equidistant from all points on the circumference of the circle

The center of a circle is a point that is equidistant from all points on the circumference of the circle. In other words, if you were to draw a line segment from the center to any point on the circle’s edge, the length of that line segment would be the same for all points on the circle.

The center is an important feature of a circle as it determines various characteristics of the circle. For example, the radius of a circle is the distance from the center to any point on the circle, while the diameter is the distance between two points on the circle passing through the center.

Finding the center of a circle can be achieved through different methods depending on the information given. If you are provided with the equation of a circle, such as (x – h)^2 + (y – k)^2 = r^2, the center can be determined by identifying the values of h and k. These values represent the x-coordinate and y-coordinate of the center, respectively.

Additionally, if you have points on the circumference of a circle, you can find the center by locating the midpoint of any chord (a line segment connecting two points on the circle). The midpoint of a chord will always coincide with the center of the circle.

Understanding the concept of the center of a circle is crucial when studying properties and relationships of circles in geometry or when solving problems involving circles in algebraic equations or coordinate geometry.

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