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The tangent of circle may be defined by using whatever of the below three characterisations.
The tangent of a circle is a line
Note. The tangent of ellipse may also be defined by using the third characterisation.
\begin{pspicture}(-5.5,-4.5)(5.5,4) \psdot(0,0) \pscircle(0,0){2} \psline[linecolor=blue](-0.5,2.875)(4,-0.5) \psline(0,0)(1.2,1.6) \psline(1.05,1.45)(1.25,1.31) \psline(1.25,1.31)(1.35,1.45) \psdot[linecolor=blue](1.2,1.6) \end{pspicture}
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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)