The Fermat Points
X13 and X14
... and a Few Relationships
by

 Markus Heisss

 Würzburg, Bavaria

  04/2024 (Last update: June 27, 2024)

    The copying of the following graphics is allowed, but without changes.

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The important information you'll find in the graphics.

 

 

First a few general facts about Fermat points, and their construction:

 

Sometimes the Fermat points are also called "Torricelli points".

 

Fermat, Torricelli
Fig. 01: First Fermat Point and its Construction

 

Source: The Book of Roger A. Johnson: "Advanced Euclidean Geometry."

 

Pierre de Fermat, inner Napoleon triangle, Nikolaus Fuss,
Fig. 02: Second Fermat Point and its Construction

 

Then the combination of both Fermat points:

 

Pierre de Fermat , Evangelista Torricelli
Fig. 03: First and Second Fermat Point

 

More information to ...

Symmedian point K = X6? [here]

Nine-point circle? [here]

Kiepert hyperbola? [here]

 

Pierre de Fermat, Evangelista Torricelli, Geometry
Fig. 04: The Centroid G lies on Angle Bisector X13NcoO

 

More information to the Napoleon triangles? [here]

 

Napoleon triangle, Torricelli point, Geometry
Fig. 05: The Centroid G lies on Angle Bisector X14NbiO

 

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Proofs:

 

first Fermat point, Napoleon circle, Napoleon triangle
Fig. 06: Proof, that G lies on the Angle Bisector X13NcoO

GX13 = GNci    ==>   The source: [here]

 

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Cite this as: 

Heisss, Markus:  From: https://triangle-geometry.jimdofree.com/fermat-points/


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Are you interested in my other geometrical discoveries?

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... to the author is maybe possible via e-mail under:   §@gmx.de   where   § = heisss

Subject: "Fermat-Points"