Center of Circle Using Midpoint Formula
If we know the coordinates of any two points on the circle that are on other sector of the circle, now we can use the midpoint formula to find the circle’s center. The formula for the midpoint is:
[(x1 + x2)/2, (y1 + y2)/2] is the midpoint (h, k)
Example: On circle, given points are A(3,4) and B(7, 8) find its center.
Solution:
Suppose we have A(3, 4) and B(7, 8), two points on the circle.
Step 1: Determine the Circle’s Two Points
Select two locations within the circle. In this instance, our selected points are A and B.
Step 2: Use the Midpoint Calculation
To determine the midpoint’s coordinates (h, k), use the following formula:
h = (x1 + x2)/2
k = (y1 + y2)/2
Enter A and B’s coordinates into the formula:
h = (3 + 7)/2 = 5
k = (4 + 8)/2 = 6
So, the midpoint (h, k) is (5, 6).
Step 3: Center is represented by midpoint coordinates
Circle’s center is represented by the coordinates (5, 6) that were found using the midpoint formula.
Step 4: Double-check using the additional points (optional)
You can verify that (5,6) is equally spaced from any additional points on the circle if there are any available points.
Step 5: Examine the Circle Equation (Alternative Method)
If the circle’s equation is known, using the formula should also produce (5, 6) as the center.
Therefore, in this case, (5, 6) is the center of the circle formed by points A(3, 4) and B(7, 8).
Related Read:
- Circle
- Area of Circle
- Chords of Circle
- Segment of Circle
- Sector of Circle
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