In the figure above with tangent line 
and secant line 
,
 |
(1)
|
(Jurgensen et al. 1963, p. 346).
The line tangent to a circle of radius 
centered at 
through 
can be found by solving the equation
![[x_0+acost; y_0+asint]·[acost; asint]=0,](/images/equations/CircleTangentLine/NumberedEquation2.svg) |
(4)
|
giving
 |
(5)
|
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 Line
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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 Line
Cite this as:
Weisstein, Eric W. "Circle Tangent Line."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CircleTangentLine.html
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