tangent of circleTangentOfCircle2007-10-24 06:21:422007-10-24 15:17:39Definitiontangent linetangent line% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
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\usepackage{pst-plot}
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\theoremstyle{definition}
\newtheorem*{thmplain}{Theorem}
\PMlinkescapeword{tangent}
The tangent of \PMlinkescapetext{circle} may be defined by using whatever of the below three characterisations.\\
The \PMlinkescapetext{{\em tangent of a circle}} is a line
\begin{itemize}
\item whose distance from the centre of the circle is equal to the radius of the circle;
\item that is perpendicular to a radius of the circle and passes through the end point of the radius lying on the circumference;
\item that has only one common point with the curve.
\end{itemize}
\textbf{Note.} The tangent of ellipse may also be defined by using the third characterisation.
\begin{center}
\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}
\end{center}