<?xml version="1.0" encoding="UTF-8"?>
<solution xmlns="http://geocentral.net">
<version>3.1</version>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>Cette solution fait partie du répertoire original de Geometria.</comments>
</envelope>
<problem>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>Ce problème fait partie du répertoire original de Geometria.</comments>
</envelope>
<text>Une première sphère est inscrite dans cette pyramide régulière, puis une autre sphère est inscrite dans la partie supérieure restante. Déterminer la position du point de contact entre la plus petite sphère et la face ABD.</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Pyramide</name>
<color>#ffff</color>
<transparent>true</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>1.0 0.0 -0.5062278801751899</coords>
</point>
<point>
<label>B</label>
<coords>-0.4999999999999997 0.8660254037844386 -0.5062278801751899</coords>
</point>
<point>
<label>C</label>
<coords>-0.5000000000000003 -0.8660254037844386 -0.5062278801751899</coords>
</point>
<point>
<label>D</label>
<coords>0.0 0.0 1.126765281680262</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.47156890097572624 -0.36943295080057037 -0.4684983278054581 0.6493468898353321</attitude>
</camera>
</figure>
</figures>
<answer>
<type>pointSet</type>
<coords>0.09672529403490243 0.16753312364548995 0.4949583067304475</coords>
</answer>
</problem>
<log>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramide</figureName>
<p0Label>D</p0Label>
<p1Label>B</p1Label>
<p2Label>A</p2Label>
</action>
<action>
<className>GCutAction</className>
<figureName>Pyramide</figureName>
<p0Label>D</p0Label>
<p1Label>E</p1Label>
<p2Label>C</p2Label>
<figure1Name>Figure1</figure1Name>
<figure2Name>Figure2</figure2Name>
</action>
<action>
<className>GDrawBisectorAction</className>
<figureName>Figure2</figureName>
<p0Label>E</p0Label>
<p1Label>C</p1Label>
<p2Label>D</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>D</p0Label>
<p1Label>E</p1Label>
<p2Label>C</p2Label>
</action>
<action>
<className>GIntersectAction</className>
<figureName>Figure2</figureName>
<p11Label>E</p11Label>
<p12Label>F</p12Label>
<p21Label>D</p21Label>
<p22Label>G</p22Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figure2</figureName>
<p1Label>H</p1Label>
<p2Label>G</p2Label>
<variableName>Rayon</variableName>
</action>
<action>
<className>GLayDistanceAction</className>
<figureName>Figure2</figureName>
<distance>Rayon</distance>
<p0Label>H</p0Label>
<p1Label>D</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>I</p0Label>
<p1Label>D</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GDrawBisectorAction</className>
<figureName>Figure2</figureName>
<p0Label>J</p0Label>
<p1Label>K</p1Label>
<p2Label>D</p2Label>
</action>
<action>
<className>GIntersectAction</className>
<figureName>Figure2</figureName>
<p11Label>D</p11Label>
<p12Label>G</p12Label>
<p21Label>J</p21Label>
<p22Label>L</p22Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>M</p0Label>
<p1Label>D</p1Label>
<p2Label>E</p2Label>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>N</value>
<figureName>Figure2</figureName>
</action>
</log>
</solution>