Interactive Circle Defined By Three Points

This interactive demonstrates how a circle is uniquely defined by three points. The general equation of the circle is given in the form of:

The values for A, B, C, and D can be solved using the following determinants.

Expanded the values are given by:

Then this can be converted to the center point form of the equation of the circle. The center point is given by:

And then the radius can be calculated using any of the three points.