Tangent plane to the ball

A plane passing through point A of a spherical surface and perpendicular to the radius drawn to point A is called a tangent plane . Point A is called a touch point .

Theorem

The tangent plane has only one common point with the ball - the point of tangency.



Evidence

Let α be the plane tangent to the ball, and A the point of tangency. Take an arbitrary point X of the plane α, different from A. Since OA is perpendicular and OX is inclined, OX> OA = R.
Therefore, point X does not belong to the ball. The theorem is proved.