Circle Tangent Line
TangentSecantTheorem
In the figure above with tangent line PT and secant line PA,
| [画像: (PA)/(PT)=(PT)/(PB) ] |
(1)
|
(Jurgensen et al. 1963, p. 346).
CircleTangentLine
The line tangent to a circle of radius a centered at (x_0,y_0)
x = x_0+acost
(2)
y = y_0+asint
(3)
through (0,0) can be found by solving the equation
![画像: [x_0+acost; y_0+asint]·[acost; asint]=0,](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/CircleTangentLine/NumberedEquation2.svg){kind=link}
giving
Two of these four solutions give tangent lines, as illustrated above, and the lengths of these lines are equal (Casey 1888, p. 29).
See also
Chord, Circle, Circle-Circle Tangents, Monge's Problem, Tangent LineExplore with Wolfram|Alpha
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References
Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., 1888.Jurgensen, R. C.; Donnelly, A. J.; and Dolciani, M. P. Th. 42 in Modern Geometry: Structure and Method. Boston, MA: Houghton-Mifflin, 1963.Referenced on Wolfram|Alpha
Circle Tangent LineCite this as:
Weisstein, Eric W. "Circle Tangent Line." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CircleTangentLine.html