 | George Bruce Halsted - Geometry - 1885 - 389 pages
...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... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...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... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...tangent to the circumference (§156). 178. COROLLARY I. CONVERSELY, a tangent to the circumference is perpendicular to the radius drawn to the point of contact. For if AB is tangent to the circumference at C, every point of AB except C lies without the circle. Hence... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...be unequal, by Proposition XXL, Book I. PROPOSITION IX.— THEOREM. 23. A straight line tangent to a circle is perpendicular to the radius drawn to the point of contact. For any other point of the tangent, as D, must lie outside of the circle, and therefore the line OD, joining... | |
 | William Chauvenet - Geometry - 1887 - 364 pages
...common with the surface of the sphere. PROPOSITION VII.—THEOREM. 36. A plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. For any other line drawn from the centre of the sphere to the plane must reach beyond the surface of the sphere,... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...line cannot intersect a circle in more than two points. PROPOSITION IX. A straight line tangent to a circle is perpendicular to the radius drawn to the point of contact. Corollary I. A perpendicular to a tangent line drawn through the point of contact must pass through... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...line cannot intersect a circle in more than two points 0 PBOPOSITION IX. A straight line tangent to a circle is perpendicular to the radius drawn to the point of contact. Corollary I. A perpendicular to a tangent line drawn through the point of contact must pass through... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...the circle, and therefore MB is a tangent to the circle at A. § 213 QED 240. .CoR. 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For, if MB is tangent to the circle at A, every point of MB, except A, is without the circle. Hence, OA... | |
 | William Elwood Byerly - 1888 - 284 pages
...infinitesimal arcs, are straight lines, and PAP 1 and P'BP are right angles, since the tangent to a circle is perpendicular to the radius drawn to the point of contact. F'P+PF=F'P'+P'F, by the definition of an ellipse. Take away from the first sum F'P + BF, and we have... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...only one tangent can drawn to a circle at a given point on the circumference. COR. 2. Any tangent to a circle is perpendicular to the radius drawn to the point of contact. COR. 3. The centre of a circle lies in the perpendicular to any tangent at the point of contact. For... | |
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A tangent to a circle is perpendicular to the radius drawn to the point of contact. 
