This online calculator finds a circle passing through three given points. It outputs the center and radius of a circle, circle equations and draws a circle on a graph. The method used to find a circle center and radius is described below the calculator.
How to find a circle passing through 3 given points
Let's recall how the equation of a circle looks like in general form:
Since all three points should belong to one circle, we can write a system of equations.
The values , and are known. Let's rearrange with respect to unknowns a, b and c.
Now we have three linear equations for three unknowns - system of linear equations with the following matrix form:
We can solve it using, for example, Gaussian elimination like in Gaussian elimination. No solution means that points are co-linear, and it is impossible to draw a circle through them.
The coordinates of a center of a circle and it's radius related to the solution like this
Knowing center and radius, we can get the equations using Equations of a circle with given center and radius in different forms