How to Find Center of Circle with Two Points?
If two points on Circumference of a Circle are given then its center is only found when these two points are on opposite segments of the circle. To find the center then follow the steps added below,
Step 1: Identify two points (A and B) on the circle that are on opposite segments of circle.
Step 2: Locate (x1, y1) and (x2, y2), their coordinates.
Step 3: Use the following formula to find their midpoint: Midpoint (h, k) = [(x1 + x2) / 2, (y1 + y2) / 2].
Step 4: The midpoint (h, k) is the center of the circle that goes through these two points.
Step 5: Check that the distance between your response and points A and B is equal.
Example: Find the center of a circle, for instance, that passes through (3, 4) and (-3, -4) that are on opposite segment of circle.
Solution:
Let center of circle is (h, k)
(h, k) is the mid-point of any two points on circumference of circle in opposite ,
(h, k) = [(-3 + 3) / 2, (4 – 4) / 2]
(h, k) = (0, 0)
(0, 0) represents the center of this circle that goes through (-3, 4) and (3, -4).
Center of Circle
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.
Table of Content
- What is Centre of a Circle?
- Center of Circle Formula
- How to Find Centre of a Circle?
- How to Find Center of Circle with Two Points?
- How to Express Center of Circle?
- Center of Circle Using Midpoint Formula