Tangent Plane Condition

Tangent Plane Condition

For sphere:

$$(x-a)^2+(y-b)^2+(z-c)^2=r^2$$

a plane:

$$Ax+By+Cz+D=0$$

is tangent to the sphere if the distance from the centre to the plane equals the radius:

$$\frac{|Aa+Bb+Cc+D|}{\sqrt{A^2+B^2+C^2}}=r$$

Usage

- Used to check whether a plane is tangent to a sphere.