 | 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... | |
 | 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... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...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.... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...straight line perpendicular to a radius at its extremity is a tangent to the circle. 254. A tangent to a circle is perpendicular to the radius drawn to the point of contact. 261. The tangents to a circle drawn from an external point are equal, and make equal angles with the... | |
 | Harvard University - Geometry - 1899 - 39 pages
...is the greater whose distance from the centre is the less. THEOREM X. A straight line tangent to a circle is perpendicular to the radius drawn to the point of contact. Corollary. A perpendicular to a tangent at the point of contact passes through the centre of the circle.... | |
 | 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.... | |
 | Webster Wells - Geometry - 1899 - 424 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. A. CB Given line AB tangent to O EC at C, and radius OC. To Prove OC±AB. (OC is the shortest line... | |
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A tangent to a circle is perpendicular to the radius drawn to the point of contact. 
