# Equation of a circle passing through 3 given points

This online calculator finds equation of a circle passing through 3 given points

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

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