The Triangle Circumcenter Calculator is a tool designed to find the circumcenter of a triangle, given the coordinates of its vertices. The circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect, and it is equidistant from all three vertices.
Formula of Triangle Circumcenter Calculator
The formula used by the Triangle Circumcenter Calculator is as follows:
x = ((x1^2 + y1^2) * (y2 - y3) + (x2^2 + y2^2) * (y3 - y1) + (x3^2 + y3^2) * (y1 - y2)) / (2 * (x1 * (y2 - y3) - y1 * (x2 - x3) + x2 * y3 - x3 * y2))
y = ((x1^2 + y1^2) * (x3 - x2) + (x2^2 + y2^2) * (x1 - x3) + (x3^2 + y3^2) * (x2 - x1)) / (2 * (x1 * (y2 - y3) - y1 * (x2 - x3) + x2 * y3 - x3 * y2))
Where:
- (x,y) are the coordinates of the circumcenter.
- (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the vertices of the triangle.
General Terms Table
| Term | Description |
|---|---|
| Circumcenter | The point equidistant from all vertices of a triangle. |
| Triangle | A polygon with three edges and three vertices. |
| Coordinates | Sets of numbers representing the position of a point in space. |
Example of Triangle Circumcenter Calculator
Suppose we have a triangle with the following vertices:
A(1,2), B(4,5), C(7,8)
Using the Triangle Circumcenter Calculator, we find the circumcenter to be (4,4)(4,4).
Most Common FAQs
A: The circumcenter is the point equidistant from all three vertices of a triangle.
A: The circumcenter is calculated using the coordinates of the vertices of the triangle and a specific formula.
A: The circumcenter plays a significant role in geometry, as it determines properties such as the circumcircle, which is a circle passing through all three vertices of the triangle.
A: Yes, depending on the triangle’s shape, the circumcenter can be inside, outside, or on the triangle itself.
A: Yes, the Triangle Calculator is applicable to all types of triangles, including equilateral, isosceles, and scalene