File:Lemoine Circle.jpg

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Original file (886 × 615 pixels, file size: 151 KB, MIME type: image/jpeg)

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Description
English: Lemione circle:

ΔABC:

  • a, b, c – sides,
  • ta, tb, tc – medians,
  • Ta, Tb, Tc – midpoints,
  • T – centroid,
  • sa, sb, sc – angle bisectors,
  • S – intersection of the angle bisectors (incenter),
  • la, lb, lc – symmedians,
  • L – intersection of the symmedians (Lemoine point),
  • oa, ob, oc – perpendicular bisectors,
  • O – intersection of the perpendicular bisectors (circumcenter),
  • K – center of LO line segment, Lemoine circle center,
  • k – Lemoine circle,
  • ra, rb, rc – parallels with sides, including Lemoine point,
  • Ra1, Ra2, Rb1, Rb2, Rc1, Rc2 – intersections of sides and ra, rb, rc parallels, all points lie at Lemoine circle
Čeština: Lemoinova kružnice:

ΔABC:

  • a, b, c – strany,
  • ta, tb, tc – těžnice,
  • Ta, Tb, Tc – paty těžnic,
  • T - těžiště,
  • sa, sb, sc – osy úhlů,
  • S – průsečík os úhlů (střed kružnice vepsané),
  • la, lb, lc – symediány,
  • L – průsečík symedián (Lemoinův bod),
  • oa, ob, oc - osy stran,
  • O – průsečík os stran (střed kružnice opsané),
  • K – střed úsečky LO, střed Lemoinovy kružnice,
  • k – Lemoinova kružnice,
  • ra, rb, rc – rovnoběžky se stranami vedené Lemoinovým bodem,
  • Ra1, Ra2, Rb1, Rb2, Rc1, Rc2 – průsečíky stran a rovnoběžek ra, rb, rc, všechny leží na Lemoinově kružnici,
Date
Source Own work
Author Lukas Sova
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Date/TimeThumbnailDimensionsUserComment
current07:32, 23 March 2009Thumbnail for version as of 07:32, 23 March 2009886 × 615 (151 KB)Lukas Sova (talk | contribs){{Information |Description={{en|1=Lemione circle: ΔABC a, b, c – sides ta, tb, tc – medians Ta, Tb, Tc – midpoints T – centroid sa, sb, sc – angle bisectors S – intersection of the angle bisectors (incenter) la, lb, lc – symmedians L – i

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