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:)
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)
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to share – to copy, distribute and transmit the work
to remix – to adapt the work
Under the following conditions:
attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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