diff --git a/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.pdf b/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.pdf
new file mode 100644
index 0000000..73317cf
Binary files /dev/null and b/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.pdf differ
diff --git a/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.svg b/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.svg
new file mode 100644
index 0000000..e0ed96d
--- /dev/null
+++ b/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.svg
@@ -0,0 +1,277 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="210mm"
+   height="148mm"
+   viewBox="0 0 210 148"
+   version="1.1"
+   id="svg8"
+   inkscape:version="0.92.2 5c3e80d, 2017-08-06"
+   sodipodi:docname="E5_rayon_terre.svg">
+  <defs
+     id="defs2">
+    <marker
+       inkscape:stockid="Arrow1Mstart"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="marker1344"
+       style="overflow:visible"
+       inkscape:isstock="true">
+      <path
+         id="path1342"
+         d="M 0,0 5,-5 -12.5,0 5,5 Z"
+         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
+         transform="matrix(0.4,0,0,0.4,4,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <marker
+       inkscape:isstock="true"
+       style="overflow:visible"
+       id="marker1286"
+       refX="0"
+       refY="0"
+       orient="auto"
+       inkscape:stockid="Arrow1Mstart"
+       inkscape:collect="always">
+      <path
+         transform="matrix(0.4,0,0,0.4,4,0)"
+         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
+         d="M 0,0 5,-5 -12.5,0 5,5 Z"
+         id="path1284"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <marker
+       inkscape:stockid="Arrow1Mstart"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="Arrow1Mstart"
+       style="overflow:visible"
+       inkscape:isstock="true"
+       inkscape:collect="always">
+      <path
+         id="path996"
+         d="M 0,0 5,-5 -12.5,0 5,5 Z"
+         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
+         transform="matrix(0.4,0,0,0.4,4,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <filter
+       inkscape:collect="always"
+       style="color-interpolation-filters:sRGB"
+       id="filter986"
+       x="-0.20633045"
+       width="1.412661"
+       y="-0.15405296"
+       height="1.3081059">
+      <feGaussianBlur
+         inkscape:collect="always"
+         stdDeviation="0.42599431"
+         id="feGaussianBlur988" />
+    </filter>
+  </defs>
+  <sodipodi:namedview
+     id="base"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:pageopacity="0.0"
+     inkscape:pageshadow="2"
+     inkscape:zoom="1.0935553"
+     inkscape:cx="134.35387"
+     inkscape:cy="314.68683"
+     inkscape:document-units="mm"
+     inkscape:current-layer="layer1"
+     showgrid="false"
+     inkscape:object-paths="true"
+     inkscape:snap-intersection-paths="true"
+     inkscape:snap-global="true"
+     showguides="false"
+     inkscape:window-width="1680"
+     inkscape:window-height="1022"
+     inkscape:window-x="1366"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1">
+    <sodipodi:guide
+       position="-12.831221,220.52593"
+       orientation="1,0"
+       id="guide1898"
+       inkscape:locked="false" />
+  </sodipodi:namedview>
+  <metadata
+     id="metadata5">
+    <rdf:RDF>
+      <cc:Work
+         rdf:about="">
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <dc:title></dc:title>
+      </cc:Work>
+    </rdf:RDF>
+  </metadata>
+  <g
+     inkscape:label="Calque 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     transform="translate(0,-149)">
+    <g
+       id="g2026"
+       transform="translate(0,-0.48389562)">
+      <g
+         transform="matrix(0.79531276,0,0,0.79531276,81.254333,81.589449)"
+         id="g1917">
+        <g
+           id="g842"
+           style="stroke-width:0.79374999;stroke-miterlimit:4;stroke-dasharray:none">
+          <path
+             id="path815"
+             style="opacity:1;vector-effect:none;fill:none;fill-opacity:1;fill-rule:nonzero;stroke:#000000;stroke-width:0.79374999;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+             sodipodi:type="arc"
+             sodipodi:cx="56.852383"
+             sodipodi:cy="148.5"
+             sodipodi:rx="37.638245"
+             sodipodi:ry="37.638245"
+             sodipodi:start="0.036596929"
+             sodipodi:end="6.2452096"
+             sodipodi:open="true"
+             d="M 94.465425,149.87714 A 37.638245,37.638245 0 0 1 56.176671,186.13218 37.638245,37.638245 0 0 1 19.214147,148.52595 37.638245,37.638245 0 0 1 56.124785,110.86879 37.638245,37.638245 0 0 1 94.46349,147.071" />
+          <g
+             transform="translate(-48.147618)"
+             id="g836"
+             style="stroke-width:0.79374999;stroke-miterlimit:4;stroke-dasharray:none">
+            <path
+               style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+               d="m 103.97172,147.47172 2.05656,2.05656"
+               id="path817"
+               inkscape:connector-curvature="0" />
+            <path
+               style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+               d="m 106.02828,147.47172 -2.05656,2.05656"
+               id="path817-3"
+               inkscape:connector-curvature="0" />
+          </g>
+        </g>
+        <path
+           style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-mid:url(#Arrow1Mstart);marker-end:url(#marker1344)"
+           d="m 79.169044,148.5 h 18.789241 20.552955 20.55295"
+           id="path844"
+           inkscape:connector-curvature="0"
+           sodipodi:nodetypes="cccc" />
+        <path
+           style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-mid:url(#marker1286);marker-end:url(#marker1286)"
+           d="m 84.350997,122.80051 h 18.237733 18.23773 18.23773"
+           id="path844-7"
+           inkscape:connector-curvature="0"
+           sodipodi:nodetypes="cccc" />
+        <path
+           style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+           d="m 89.294491,129.41736 11.310069,-6.61685"
+           id="path890"
+           inkscape:connector-curvature="0"
+           sodipodi:nodetypes="cc" />
+        <path
+           style="fill:none;stroke:#000000;stroke-width:1.05833328;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;filter:url(#filter986)"
+           d="m 84.350997,122.80051 4.955092,6.63659"
+           id="path892"
+           inkscape:connector-curvature="0" />
+        <path
+           style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+           d="M 94.41159,147.12593 H 79.169045 v 2.74815 H 94.41159"
+           id="path1864"
+           inkscape:connector-curvature="0" />
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+           x="96.537186"
+           y="155.70245"
+           id="text1881"><tspan
+             sodipodi:role="line"
+             id="tspan1879"
+             x="96.537186"
+             y="155.70245"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Syrène</tspan></text>
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+           x="95.569389"
+           y="132.23354"
+           id="text1885"><tspan
+             sodipodi:role="line"
+             id="tspan1883"
+             x="95.569389"
+             y="132.23354"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Alexandrie</tspan></text>
+        <path
+           style="fill:none;stroke:#000000;stroke-width:0.5291667;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+           d="M 89.294424,129.41725 56.85238,148.5 H 94.6016"
+           id="path1900"
+           inkscape:connector-curvature="0" />
+      </g>
+      <g
+         id="g1989">
+        <flowRoot
+           xml:space="preserve"
+           id="flowRoot1919"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none"
+           transform="matrix(0.26458333,0,0,0.26458333,0,155.27276)"><flowRegion
+             id="flowRegion1921"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start"><rect
+               id="rect1923"
+               width="251.69719"
+               height="494.91534"
+               x="42.676441"
+               y="52.425682"
+               style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start" /></flowRegion><flowPara
+             id="flowPara1925">	Vers l'an 200 avant Jésus- Christ, des voyageurs dirent à Eratosthène, géomètre de l'école d'Alexandrie, que le premier jour de l'été, à Syène ( Prés de l'actuel Assouan, en haute Égypte ), rayons du soleil à midi étaient verticaux : Ils pouvaient éclairer le fond d'un puits. Or ce même jour, le soleil n'était pas au Zénith à Alexandrie puisqu'un piquet de 1m de haut, planté verticalement avait une ombre de 12,3 cm.</flowPara><flowPara
+             id="flowPara1927" /><flowPara
+             id="flowPara1929">Eratosthène savait également que les caravanes des chameaux partant de Syène, en parcourant 100 stades par jour ( le stade équivaut à 160m ), mettaient 50 jours pour arriver à Alexandrie ( Ville située au nord de Syène ).Enfin, il supposa que le soleil était assez éloigné pour que ses rayons lumineux frappent la surface terrestre en faisceaux parallèles.A partir de toutes ces informations, Eratosthène réussit à déterminer la valeur du rayon de la Terre.</flowPara><flowPara
+             id="flowPara1931" /><flowPara
+             id="flowPara1933" /><flowPara
+             id="flowPara1935" /><flowPara
+             id="flowPara1937" /></flowRoot>        <flowRoot
+           xml:space="preserve"
+           id="flowRoot1951"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:16px;line-height:1.25;font-family:Consolas, 'Liberation Mono', Menlo, Courier, monospace;-inkscape-font-specification:'Consolas, Liberation Mono, Menlo, Courier, monospace';text-align:justify;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none"
+           transform="matrix(0.26458333,0,0,0.26458333,3.3872696,156.98428)"><flowRegion
+             id="flowRegion1953"
+             style="text-align:justify;text-anchor:start"><rect
+               id="rect1955"
+               width="384.98282"
+               height="147.2262"
+               x="343.83264"
+               y="341.73132"
+               style="text-align:justify;text-anchor:start" /></flowRegion><flowPara
+             id="flowPara1957"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">1) Reporter les informations du texte sur le schéma.</flowPara><flowPara
+             id="flowPara1959"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">2) Calculer l'angle que fait les rayons du soleil avec le piquet planté à Alexandrie.</flowPara><flowPara
+             id="flowPara1961"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">3) Quel angle y a-t-il entre Alexandrie, le centre de la terre et Syrène?</flowPara><flowPara
+             id="flowPara1963"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">4) Calculer la circonférence de la terre.</flowPara><flowPara
+             id="flowPara1965"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">5) En déduire le rayon de la terre.</flowPara></flowRoot>      </g>
+    </g>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+       x="75.414207"
+       y="161.02531"
+       id="text1969"><tspan
+         sodipodi:role="line"
+         id="tspan1967"
+         x="75.414207"
+         y="161.02531"
+         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Calculer la rayon de la terre</tspan></text>
+  </g>
+</svg>
diff --git a/3e/Geometrie/Triangle_rectangle/index.rst b/3e/Geometrie/Triangle_rectangle/index.rst
index e3e3e38..7bc71f2 100644
--- a/3e/Geometrie/Triangle_rectangle/index.rst
+++ b/3e/Geometrie/Triangle_rectangle/index.rst
@@ -2,7 +2,7 @@ Théorème de Pythagore et découverte du cosinus avec les 3e pour l'année 2017
 #################################################################################
 
 :date: 2018-01-02
-:modified: 2018-02-12
+:modified: 2018-02-19
 :tags: Geometrie, Pythagore, Trigonométrie
 :category: 3e
 :authors: Bertrand Benjamin
@@ -44,3 +44,7 @@ Sur le cahier de bord, on écrit la définition du cos.
 
 Même chose que l'étape d'avant mais avec des angles quelconques.
 
+Étape 5: Circonférence de la terre
+----------------------------------
+
+Tache complexe décompléxifiée pour `calculer le rayon de la terre <./E5_rayon_terre.pdf>`_