<?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>This is the solution of a sample Geometria problem.</comments>
</envelope>
<problem>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>This is a sample Geometria problem.</comments>
</envelope>
<text>This block has the shape of two regular pyramids joined at their bases. Some of its lower part will be cut off and the remaining fragment will be used to support the ceiling of a room. The height of the room equals the block&#39;s longest edge. Find the plane of the cut.</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Block</name>
<color>#ccff</color>
<transparent>false</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>0.9999999999999998 0.0 0.0</coords>
</point>
<point>
<label>B</label>
<coords>0.30901699437494723 0.9510565162951535 0.0</coords>
</point>
<point>
<label>C</label>
<coords>-0.8090169943749476 0.5877852522924732 0.0</coords>
</point>
<point>
<label>F</label>
<coords>0.0 0.0 1.6329931618554518</coords>
</point>
<point>
<label>D</label>
<coords>-0.8090169943749477 -0.587785252292473 0.0</coords>
</point>
<point>
<label>E</label>
<coords>0.309016994374947 -0.9510565162951536 0.0</coords>
</point>
<point>
<label>G</label>
<coords>0.0 0.0 -1.6329931618554518</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.5776679660403664 -0.08700769102190056 -0.155600704687259 0.7965662580191633</attitude>
</camera>
</figure>
</figures>
<answer>
<type>fixedPlane</type>
<coords>-0.6693774736545859 0.4863312018988447 -0.281861053657224</coords>
<coords>-0.669377473654586 0.0 -0.28186105365722414</coords>
<coords>0.8273960600441423 0.0 -0.28186105365722414</coords>
</answer>
</problem>
<log>
<action>
<className>GCutAction</className>
<figureName>Block</figureName>
<p0Label>F</p0Label>
<p1Label>D</p1Label>
<p2Label>G</p2Label>
<figure1Name>Figure1</figure1Name>
<figure2Name>Figure2</figure2Name>
</action>
<action>
<className>GDrawLineAction</className>
<figureName>Figure2</figureName>
<p1Label>F</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figure2</figureName>
<p1Label>D</p1Label>
<p2Label>F</p2Label>
<variableName>Height</variableName>
</action>
<action>
<className>GLayDistanceAction</className>
<figureName>Figure2</figureName>
<distance>Height</distance>
<p0Label>F</p0Label>
<p1Label>F</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>I</p0Label>
<p1Label>F</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<fLabel1>G</fLabel1>
<fLabel2>B</fLabel2>
<fLabel3>H</fLabel3>
<p0Label>K</p0Label>
<p1Label>H</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>J,K,L</value>
<figureName>Figure2</figureName>
</action>
</log>
</solution>