Circle Through Three Given Points

Circle Through Three Given Points

For three non-collinear points $$(x_1,y_1)$$, $$(x_2,y_2)$$ and $$(x_3,y_3)$$:

$$ \begin{vmatrix}x^2+y^2&x&y&1\\x_1^2+y_1^2&x_1&y_1&1\\x_2^2+y_2^2&x_2&y_2&1\\x_3^2+y_3^2&x_3&y_3&1\end{vmatrix}=0 $$

Usage

- Used to directly obtain the equation of the unique circle passing through three non-collinear points.