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Circle Tangent Line


TangentSecantTheorem

In the figure above with tangent line PT and secant line PA,

 (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

 [x_0+acost; y_0+asint]·[acost; asint]=0,
(4)

giving

 t=+/-cos^(-1)((-ax_0+/-y_0sqrt(x_0^2+y_0^2-a^2))/(x_0^2+y_0^2)).
(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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