How to Express Center of Circle?

If you are given an equation for a circle or just two points on it, there are multiple ways to determine its center. Some of the common ways are,

Using Chords

Line segments that join two points on a circle are called chords. A chord is referred to as a diameter if it runs through the center of the circle. The circle’s center is the midpoint of a diameter. Given the endpoints of a chord (diameter), (x₁, y₁) and (x₂, y₂) the formula to find the mid point of chord is,

(x₁ + x₂/2, y₁ + y₂/2) is the midpoint.

Using of Secant

A line that crosses a circle twice is called a secant of a circle. The line segment that results when a secant passes through the circle’s center is called a diameter. The center of the circle is the midpoint of the diameter, just like in the chord case.

Using Overlapping Circles

Center of the given circle can be found when working with overlapping circles by using the point of intersection of their common chord, which is a line connecting two points on a circle.

Using Tangents

Radius at the tangency point of a circle is perpendicular to the tangent line. Therefore, the center of the circle can be found by measuring the midpoint of the line segment that connects the tangent line and the point of tangency to the center.

When Equation of Circle is Given to Us

A circle’s standard equation is (x – h)²+(y – k)² = r², where the radius is denoted by r and the circle’s center by (h, k). Therefore, you can determine the values of h and k, which stand for the center’s coordinates, from the provided equation.

Center of a Circle is defined as a point inside the circle that is equidistant from all the points on the circumference of the circle. It is generally denoted using (h, k) points and is the point from where all the radius passes. Cente of the circle is defined as the mid-point of the end point of the diameter of the circle.

In this article, we will learn about, center of a circle, its formulas, and examples in detail.