Image:Fermat Point Proof.svg

[edit] Summary

Proving the construction of Fermat Point is valid:

We have to prove the three lines constructed are concurrent. The red and blue triangle are congruent by S.A.S. , and hence the angles in the same segment are the same, which shows that there are two cyclic quadrilaterals. Thus the last four points are also concyclic, and by angle in the same segment the last line is a straight line.

N.B. all information are included in the metadata of this svg file.

[edit] Source

The source is licensed under the same license as the image. Feel free to edit, fix, or improve it!

[edit] fermat_point_proof.euk

frame(-2.8, -6, 8.2, 7.5)
B C A triangle(6, 75:, 35:)
C B P equilateral
A C Q equilateral
B A R equilateral
s = segment(A, P)
t = segment(B, Q)
u = segment(C, R)
c = circle(B, A, R)
d = circle(A, C, Q)
e = circle(C, B, P)
F = intersection(line(A, P), line(B, Q))

color(green)
draw(c)
color(cyan)
draw(d)
color(blue)
draw(t)
draw(segment(A, Q))
draw(segment(A, B))
mark(segment(A, B), simple)
mark(segment(A, Q), double)
mark(B, A, Q, simple, 1.2)
color(red)
draw(u)
draw(segment(A, R))
draw(segment(A, C))
mark(segment(A, R), simple)
mark(segment(A, C), double)
mark(R, A, C, simple, 0.8)
color(black)
draw(s)
draw(segment(B, R))
draw(segment(C, Q))
draw(C, B, P)
draw(e, dashed)
draw(F, dot, 1.3)
mark(segment(B, R), simple)
mark(segment(C, Q), double)
mark(segment(B, C), triple)
mark(segment(B, P), triple)
mark(segment(C, P), triple)
mark(C, R, A, double, 1.5)
mark(Q, B, A, double, 1.5)
mark(A, Q, B, triple, 1.5)
mark(A, C, R, triple, 1.5)
mark(B, F, P, dot, 0.8)
mark(B, C, P, dot, 0.8)
label(F, 0.5, 0:)
label(A, 0.5, 90:)
label(B, 0.5, 225:)
label(C, 0.5, 330:)
label(P, 0.3, 270:)
label(Q, 0.3, 0:)
label(R, 0.3, 90:)

[edit] Instruction

1. Run eukleides and compile it into en:PSTricks.
2. Paste the resulting code in the following en:TeX file and compile it into eps.

\documentclass{article}
\usepackage{pstricks}
\usepackage{color}

\begin{document}
\pagestyle{empty}
\colorbox{white}{

%Paste the code here

}
\end{document}

1. Import the eps file using en:Scribus. (Remember to install en:ghostscript also and configure the path to ghostscript correctly in Scribus's Preferences)
2. And then export it to en:svg.
3. Post-process using en:Inkscape.

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license". Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/- This file is licensed under the Creative Commons Attribution ShareAlike license versions 2.5, 2.0, and 1.0 العربية | Български | Català | Česky | Dansk | Deutsch | English | Español | Euskara | فارسی | Français | עברית | Italiano | 日本語 | 한국어 | Lietuvių | Nederlands | Polski | Português | Русский | Svenska | தமிழ் | Türkçe | 中文 | 中文 | +/- You may select the license of your choice.

• Fermat point