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.
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