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" A tangent to a circle is perpendicular to the radius drawn to the point of contact. "
An Elementary Treatise on Plane and Solid Geometry - Page 38
by Benjamin Peirce - 1871 - 150 pages
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...and AB is 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. ACB Let the line AB be tangent to the circle EC. To prove that AB is perpendicular to the radius OC...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...circles, of two 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...
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Elements of the Integral Calculus: With a Key to the Solution of ...

William Elwood Byerly - Calculus, Integral - 1895 - 298 pages
...PA and P'B being 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...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...straight line 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...
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The New Metal Worker Pattern Book: A Treatise on the Principles and Practice ...

George Watson Kittredge - Sheet metal working - 1896 - 448 pages
...or other curve is a straight line which touches it at only one point, as ED and AC, Fig. 35. Every tangent to a circle is perpendicular to the radius drawn to the point of tangency. Thus ED is perpendicular to FD and AC to FB. Fig. 34.— A Quadrant. Fig. 35. — Tangents....
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...every point of 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...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...without the O, 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. ACB Given line AB tangent to O EC at C, and radius OC. To Prove OC±AB. (OC is the shortest line that...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 490 pages
...If a line is perpendicular to a radius at its extremity, it is a tangent to the circle. Converse: A tangent to a circle is perpendicular to the radius drawn to the point of tangency. To prove the converse: Draw a 0 and a tangent. Draw a radius to point of tangency. Is the...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...except D, is without theO. . , . AB is a tangent to the O. (?) QED Proposition 112. Theorem. 145. A tangent to a circle is perpendicular to the radius drawn to the point of contact. HINT. Prove that the radius is the shortest line that can be drawn from the centre to the tangent....
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...is without 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 J. to MB (§ 98) ; that is, MB is -L to...
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