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File:The smallest enclosing disk of points in the plane is unique.svg

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Summary

Description
English: Geometrical demonstration for smallest-circle problem.
Date
Source Own work
Author Siddharthist
SVG development
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This vector image was created with LaTeX.
Source code
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LaTeX code

Source code
\begin{tikzpicture}[scale=1.5]
  \def\r{1}

  % origin
  \node[circle] (O) at (-2,-2) {$\vec{0}$};

  % circles and their centers
  \node[scale=0.01] (D1) at (\r,0) {$\cdot$};
  \node[scale=0.01] (D2) at (0,\r) {$\cdot$};
  \node[scale=0.01] (D3) at ($(D1)!0.5!(D2)$) {};
  \draw (D1) circle (2*\r cm);
  \draw (D2) circle (2*\r cm);
  \draw[->] (O) -- node[below, sloped, near start] {$\vec{z}_1$} (D1);
  \draw[->] (O) -- node[above, sloped, near start] {$\vec{z}_2$} (D2);
  % \draw[->] (O) -- (D3);
  \draw[->] (O) -- node[near end, above, sloped] {$\frac 12 (\vec{z}_1+\vec{z}_2)$} (D3);

  % The two copies of a
  \draw (D1) -- node[near start, above, sloped] {$a$} (D2);
  \draw (D1) -- node[near end, above, sloped] {$a$} (D2);

  % The triangle's other leg
  \node[scale=0.01] (X) at ($ 1.83*({\r},{\r}) $) {};
  \node[scale=0.1] (D3) at ($(D1)!0.5!(D2)$) {}; % center of new circle

  % triangle's two hypotenuses
  \draw (D2) -- node[above, sloped] {$r$} (X);
  % \draw (D1) -- node[below right] {$r$} (X);
  \draw (D3) -- node[midway, sloped, below] {$\sqrt{r^2-a^2}$} (X);

  % the new, smaller circle
  \draw[dashed] (D3) circle (1.85*\r);

  % some points
  % \node[scale=2] at (0.5,1.5) {$\cdot$};
  % \node[scale=2] at (0.3,-0.2) {$\cdot$};
  % \node[scale=2] at (0.2,1.0) {$\cdot$};
  % \node[scale=2] at (1.4,0.8) {$\cdot$};
  % \node[scale=2] at (0.7,-0.4) {$\cdot$};
  % \node[scale=2] at (-0.4,0.1) {$\cdot$};
\end{tikzpicture}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • 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.

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14 November 2017

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Date/TimeThumbnailDimensionsUserComment
current01:13, 14 November 2017Thumbnail for version as of 01:13, 14 November 2017287 × 278 (29 KB)SiddharthistCross-wiki upload from en.wikipedia.org

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