medial triangle
MedialTriangle
2002-12-02 00:41:26
2006-07-25 11:20:02
Definition
Spieker center
Spieker circle
medial circle
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\PMlinkescapeword{property}
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The \emph{medial triangle} of a triangle $\triangle ABC$ is the triangle formed by joining the midpoints of the sides of the triangle $\triangle ABC.$
\begin{center}
\includegraphics{med.eps}
\end{center}
Here, $\triangle A'B'C'$ is the medial triangle.
The incircle of the medial triangle is called the \emph{Spieker circle} and the incenter is called the \emph{Spieker center}.
The circumcircle of the medial triangle is called the \emph{medial circle}.
An important property of the medial triangle is that the medial triangle $\triangle A'B'C'$ of the medial triangle $\triangle DEF$ of $\triangle ABC$ is similar to $\triangle ABC.$
\begin{center}
\includegraphics{med1.eps}
\end{center}