Bonjour,
Voici une figure ajustable (plugin). On peut déplmacer la point M
Il semblerait que les angles aient des valeurs simples, mais je ne sais pas le démontrer
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"[
www.w3.org];
<html xmlns="[
www.w3.org];
<head>
<title>Sangaku - GeoGebra Feuille de travail dynamique</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="GeoGebra" />
<style type="text/css"><!--body { font-family:Arial,Helvetica,sans-serif; margin-left:40px }--></style>
</head>
<body>
<table border="0" width="610">
<tr><td>
<h2>Sangaku</h2>
<p>
</p>
<applet name="ggbApplet" code="geogebra.GeoGebraApplet" archive="geogebra.jar"
codebase="[
www.geogebra.org];
width="610" height="578"mayscript="true">
<param name="ggbBase64" value="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"/>
<param name="image" value="[
www.geogebra.org]; />
<param name="boxborder" value="false" />
<param name="centerimage" value="true" />
<param name="java_arguments" value="-Xmx512m -Djnlp.packEnabled=true" />
<param name="cache_archive" value="geogebra.jar, geogebra_main.jar, geogebra_gui.jar, geogebra_cas.jar, geogebra_export.jar, geogebra_properties.jar" />
<param name="cache_version" value="3.2.46.0, 3.2.46.0, 3.2.46.0, 3.2.46.0, 3.2.46.0, 3.2.46.0" />
<param name="framePossible" value="true" />
<param name="showResetIcon" value="false" />
<param name="showAnimationButton" value="true" />
<param name="enableRightClick" value="false" />
<param name="errorDialogsActive" value="true" />
<param name="enableLabelDrags" value="false" />
<param name="showMenuBar" value="true" />
<param name="showToolBar" value="true" />
<param name="showToolBarHelp" value="false" />
<param name="showAlgebraInput" value="false" />
<param name="allowRescaling" value="true" />
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (<a href="[
java.sun.com] here to install Java now</a>)
</applet>
<p>
</p>
<p><span style="font-size:small">jacquot, Créé avec <a href="[
www.geogebra.org]; target="_blank" >GeoGebra</a></span></p></td></tr>
</table></body>
</html>