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" Any line or plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. "
Chauvenet's Treatise on Elementary Geometry - Page 268
by William Chauvenet - 1887 - 322 pages
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...proposed point let a radius be drawn, and a plane perpendicular to the radius will be the tangent plane. For any other line drawn from the centre of the sphere to meet this plane is necessarily greater than the radius of the sphere which is the perpendicular upon...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 284 pages
...therefore tangent to it at the point D (D. 8). Therefore, etc. Cor. Conversely. — A tangent to the circle is perpendicular to the radius drawn to the point of contact. For any line, as CE, is greater than CF, or its equal CD; hence, CD, being the shortest line from C to the...
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Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 172 pages
...A. Hence every other point in AB except A lies without the circumference. Conversely. Every tangent is perpendicular to the radius drawn to the point of contact. For the radius OA is the shortest line that can be drawn to AB ; it is therefore perpendicular to it. COR....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...A in common with the sphere, and is consequently tangent to the sphere. 44. Corollary. Conversely, a plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. For, since every point of the plane except the point of contact is without the sphere, the radius drawn...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...point in common with the sphere; (?) hence, MN is tangent to the sphere at A. 449. Corollaries. 1. A plane tangent to a sphere is perpendicular to the radius drawn to the piint of contact. (?) 2. A straight line tangent to a circle of a sphere lies in the plane tangent...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...is without the sphere, except P. .'. MN is tangent to the sphere at P. § 673 QED 689. COROLLARY 1. A plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. 690. COR. 2. Л straight line tangent to a circle of a sphere lies in a plane tangent to the sphere...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...extremity is tangent to the sphere (§ 725). 763. Cor. 2. Conversely, every plane or line tangent to the sphere is perpendicular to the radius drawn to the point of contact. THEOREM XIV. 764. All lines tangent to a sphere from the same external point are equal, and touch the...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...at its extremity is tangent to the sphere. 630. INVERSE OF 628. Every plane or line tangent to the sphere is perpendicular to the radius drawn to the point of contact. For since every point of the plane or line, except the point of contact, is without the sphere, the radius...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...at its extremity is tangent to the sphere. 630. INVERSE OF 628. Every plane or line tangent to the sphere is perpendicular to the radius drawn to the point of contact. For since every point of the plane or line, except the point of contact, is without the sphere, the radius...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...plane is tangent to the surface (§ 621). 639. COROLLARY. CONVERSELY, a plane tangent to the surface of a sphere is perpendicular to the radius drawn to the point of contact. PROPOSITION IX. THEOREM. 640. A. sphere may be circumscribed about any tetrdedrnn. A Let ABCD be any...
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