 | William Chauvenet - 1893 - 340 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... | |
 | Webster Wells - Geometry - 1894 - 256 pages
...tangent to the circle. (§ 149.) PROPOSITION XV. THEOREM. 170. (Converse of Prop. XIV.) A tangent to a circle is perpendicular to the radius drawn to the point of contact. ACS To prove that AB is perpendicular to the radius OC drawn to the point of contact. If AB is tangent... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...chords that which is at a less distance from the centre is the greater. 181. Theorem. A tangent to a circle is perpendicular to the radius drawn to the point of contact. 182. Theorem. A perpendicular to a radius at its end is a tangent to the circle. 183. Theorem. A perpendicular... | |
 | American Mathematical Society - Mathematics - 1903 - 712 pages
...assumed and frequently applied in dealing with Jimiting cases. Thus the theorem that the tangent to a circle is perpendicular to the radius drawn to the point of contact (Proposition 44) is derived by considering the limiting value of the exterior angle of the isosceles... | |
 | William Elwood Byerly - Calculus, Integral - 1895 - 298 pages
...infinitesimal arcs, are straight lines, and PAT 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... | |
 | John Macnie - Geometry - 1895 - 390 pages
...tangent to CEF at C, QED (188) (since C is the only point in AB not without CEF.) 191. COE. 1. A tangent is perpendicular to the radius drawn to the point of contact. For OC must be less than any other line drawn from 91 192. COB. 2. A perpendicular to a tangent at the... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...perpendicular to a radius at its extremity is a tangent to the circle. 240. Cor. 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. 241. Cor. 2. A perpendicular to a tangent at the point of contact passes through the centre of the... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...AB, except C, lies without the circle. PROPOSITION XVII. THEOREM. 169. CONVERSELY—»4 tangent to a circle is perpendicular to the radius drawn to the point of contact. Given—AB tangent to the circle CE. To Prove—AB perpendicular to the radius OC. Dem.—Draw OD to... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...and AB is tangent to the O. (§ 149) PROP. XV. THEOREM. 170. (Converse of Prop. XIV.) A tangent to a circle is perpendicular to the radius drawn to the point of contact. ACS Given line AB tangent to O EC at C, and radius OC. To Prove OC±AB. (OC is the shortest line that... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...the circle, and therefore MB is a tangent to the circle at A. § 220 QED 254. COR. 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For OA is the shortest line from 0 to MB, and is therefore _L to MB (§ 98); that is, MB is _L to OA. 255.... | |
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A tangent to a circle is perpendicular to the radius drawn to the point of contact. 
