Circle Through Origin and Tangent to a Given Line

Circle Through Origin and Tangent to a Given Line

For a circle:

$$x^2+y^2+2gx+2fy=0$$

tangent to:

$$Ax+By+C=0$$

the centre $$(-g,-f)$$ must satisfy:

$$\frac{| -Ag-Bf+C |}{\sqrt{A^2+B^2}}=\sqrt{g^2+f^2}$$

Usage

- Used to determine circles passing through the origin and tangent to a specified line.