circumscribeCircumscribe2006-11-15 18:13:082007-08-02 18:45:10Definition% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{pstricks}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
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To \emph{circumscribe} a regular polygon (such as a triangle, square, pentagon, etc.) or a cyclic quadrilateral, is to enclose it in a circle so that the vertices of the polygon are on the circumference of the circle.
For example, a circumscribed square:
\begin{center}
\begin{pspicture}(-3,-3)(3,3)
\pscircle(0,0){2.13}
\pspolygon(1.5,1.5)(-1.5,1.5)(-1.5,-1.5)(1.5,-1.5)
\end{pspicture}
\end{center}
One more example, a circumscribed pentagon.
\begin{center}
\begin{pspicture}(-2,-2)(2,2)
\pscircle(0,0){1.702}
\pspolygon(0,1.702)(-1.619,0.526)(-1,-1.377)(1,-1.377)(1.619,0.526)
\end{pspicture}
\end{center}