 | George Albert Wentworth - Geometry - 1888 - 272 pages
...CC'. Proof. A -L to AB, drawn through the point O, passes through the centres C and C', § 241 (a -L to a tangent at the point of contact passes through the centre of the circle). ,~. the line CC', having two points in common with this -L must coincide with it. .-. O is in the straight... | |
 | George Albert Wentworth - Geometry, Plane - 1892 - 266 pages
...Proof. A _L to AB, drawn through the point 0, passes through the centres C and C", § 241 (<<.!/"<'. tangent at the point of contact passes through the centre of the circle). .-. the line CC', having two points in common with this J_ must coincide with it. .'. O is in the straight... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...whatever is true of the ellipse is true of the circle (as §§ 40-43, 44), but not vice versa, as, a perpendicular to a tangent at the point of contact passes through the centre, equal chords are equally distant from the centre, etc. Many of the properties of the ellipse and hyperbola,... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...contact. 182. Theorem. A perpendicular to a radius at its end is a tangent to the circle. 183. Theorem. A perpendicular to a tangent at the point of contact passes through the centre. 184. Theorem. The tangents drawn from an exterior point to a circle are equal. 185. Theorem. The line... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...COROLLARY. At any point in a circumference, one, and only one, tangent can be drawn and a straight line perpendicular to a tangent at the point of contact passes through the center. Ex. 100. In the figure at the right, AE and BC are parallel, and MO is a transversal. BO bisects... | |
 | John Macnie - Geometry - 1895 - 386 pages
...191. COR. 1. A tangent is perpendicular to the radius drawn to the point of contact. 192. COR. 2. A perpendicular to a tangent at the point of contact passes through the center of the circle. ' For otherwise there could be two perpendiculars to the tangent at that point... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...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 circle. 242. Cor. 3. A perpendicular let fall from the centre of a circle upon a tangent to the circle passes... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...oblique line equal to radius would fix a second point common to tangent and circle.] 169. COR. 2. The perpendicular to a tangent at the point of contact passes through the center of the circle. Ex. 1. If a radius and a tangent are perpendicular, they intersect at the point... | |
 | Harvard University - Geometry - 1899 - 39 pages
...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. THEOREM XI. THEOREM XII. Two parallel straight lines intercept equal arcs on a circumference. THEOREM XIII.... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...the shortest line that can be drawn from the centre to the tangent. Proposition 113. Theorem. 146. A perpendicular to a tangent at the point of contact passes through the centre of the circle. HINT. Draw a radius to the point of contact, and consult Prop. 112 and Prop. 1. COB. A perpendicular... | |
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Hence, conversely, a line drawn perpendicular to a tangent, at the point of contact, passes through the centre of the circle. 
