File:Fermat Point Proof.svg

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Summary
DescriptionFermat Point Proof.svg |
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. |
Date | 11 March 2006 (original upload date) |
Source | No machine-readable source provided. Own work assumed (based on copyright claims). |
Author | No machine-readable author provided. Lemontea~commonswiki assumed (based on copyright claims). |
Source
The source is licensed under the same license as the image. Feel free to edit, fix, or improve it!
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:)
Instruction
- Run eukleides and compile it into en:PSTricks.
- 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}
- Import the eps file using en:Scribus. (Remember to install en:ghostscript also and configure the path to ghostscript correctly in Scribus's Preferences)
- And then export it to en:svg.
- Post-process using en:Inkscape.
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |



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11 March 2006
29,783 byte
image/svg+xml
4e3e1553450c2fa917c944a475a6e636cc4ea052
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 02:22, 11 March 2006 | ![]() | 350 × 400 (29 KB) | wikimediacommons>Lemontea~commonswiki | 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 cycl |
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