Tangent plane to the sphere

Property — Tangent plane to the sphere

The plane tangent to the sphere at one of its points $D$ is perpendicular to the radius $CD$ (where $C$ is the centre), so it has equation $(\vec S - \vec D)\cdot\vec{CD}=0.$

The vector $\vec{CD}$ acts as the normal of the tangent plane: tangency at $D$ is equivalent to requiring the plane to be perpendicular to the radius at that point.

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Topics: Analytic geometry in space
Concepts: Plane · Tangent plane · Sphere
Skills: Analytic geometry · Using formulae