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'medial triangle'
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| Title of object: |
medial triangle |
| Canonical Name: |
MedialTriangle |
| Type: |
Definition |
| Created on: |
2002-12-02 00:41:26 |
| Modified on: |
2006-07-25 11:17:01 |
| Classification: |
msc:51-00 |
| Defines: |
Spieker center, Spieker circle, medial circle |
| Synonyms: |
medial triangle=auxiliary triangle |
Revision comment (for changes between this and next version):
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
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Content:
\PMlinkescapeword{property}
The \emph{medial triangle} of a 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} |
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