PlanetMath: medial triangle

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medial triangle

(Definition)

The medial triangle of a triangle $\triangle ABC$ is the triangle formed by joining the midpoints of the sides of the triangle $\triangle ABC.$

$\includegraphics{med.eps}$

Here, $\triangle A'B'C'$ is the medial triangle. The incircle of the medial triangle is called the Spieker circle and the incenter is called the Spieker center. The circumcircle of the medial triangle is called the 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 $\triangle ABC.$

$\includegraphics{med1.eps}$

"medial triangle" is owned by yark. [ full author list (2) | owner history (1) ]

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Other names:

auxiliary triangle

Also defines:

Spieker center, Spieker circle, medial circle

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Cross-references: circumcircle, incenter, incircle, sides, midpoints, triangle
There is 1 reference to this entry.

This is version 5 of medial triangle, born on 2002-12-02, modified 2006-07-25.
Object id is 3640, canonical name is MedialTriangle.
Accessed 6566 times total.

Classification:

AMS MSC:

51-00 (Geometry :: General reference works )

Pending Errata and Addenda

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