@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr: a skos:ConceptScheme .
psr:-GKWK9C3G-P
  skos:prefLabel "géométrie euclidienne"@fr, "Euclidean geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-FX7WMH6H-5 .

psr:-FX7WMH6H-5
  skos:definition """Le théorème japonais de Carnot est un théorème de géométrie euclidienne dû à Lazare Nicolas Marguerite Carnot, portant sur une égalité algébrique de distances dans une construction faisant appel au cercle inscrit et au cercle circonscrit à un triangle. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_japonais_de_Carnot">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_japonais_de_Carnot</a>)"""@fr, """In Euclidean geometry, <b>Carnot's theorem</b> states that the sum of the signed distances from the circumcenter <i>D</i> to the sides of an arbitrary triangle <i>ABC</i> is 
         <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle DF+DG+DH=R+r,\\\\ }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>D</mi>
         <mi>F</mi>
         <mo>+</mo>
         <mi>D</mi>
         <mi>G</mi>
         <mo>+</mo>
         <mi>D</mi>
         <mi>H</mi>
         <mo>=</mo>
         <mi>R</mi>
         <mo>+</mo>
         <mi>r</mi>
         <mo>,</mo>
         <mtext> </mtext>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle DF+DG+DH=R+r,\\\\ }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14f1eb98bbe580fb42e0b147b408f44bd7a42ce3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.451ex; height:2.509ex;" alt="DF + DG + DH = R + r,\\\\ "></span></dd></dl>
         where <i>r</i> is the inradius and <i>R</i> is the circumradius of the triangle. Here the sign of the distances is taken to be negative if and only if the open line segment <i>DX</i> (<i>X</i> = <i>F</i>, <i>G</i>, <i>H</i>) lies completely outside the triangle. In the diagram, <i>DF</i> is negative and both <i>DG</i> and <i>DH</i> are positive.
         
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Carnot%27s_theorem_(inradius,_circumradius)">https://en.wikipedia.org/wiki/Carnot%27s_theorem_(inradius,_circumradius)</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-GKWK9C3G-P ;
  skos:prefLabel "Carnot's theorem"@en, "théorème japonais de Carnot"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_japonais_de_Carnot>, <https://en.wikipedia.org/wiki/Carnot%27s_theorem_(inradius,_circumradius)> .