<?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>Find a plane that cuts off the pyramid a volume equal to the volume of the cube.</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Cube</name>
<color>#339900</color>
<transparent>false</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>-0.5 -0.5 -0.5</coords>
</point>
<point>
<label>B</label>
<coords>0.5 -0.5 -0.5</coords>
</point>
<point>
<label>C</label>
<coords>0.5 0.5 -0.5</coords>
</point>
<point>
<label>E</label>
<coords>-0.5 -0.5 0.5</coords>
</point>
<point>
<label>D</label>
<coords>-0.5 0.5 -0.5</coords>
</point>
<point>
<label>F</label>
<coords>0.5 -0.5 0.5</coords>
</point>
<point>
<label>G</label>
<coords>0.5 0.5 0.5</coords>
</point>
<point>
<label>H</label>
<coords>-0.5 0.5 0.5</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.5328608041697043 -0.3348186344436886 -0.4134665796294599 0.6580282918981487</attitude>
</camera>
</figure>
<figure>
<name>Pyramid</name>
<color>#ff6600</color>
<transparent>false</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>0.996180339887499 0.0 -0.5062278801751902</coords>
</point>
<point>
<label>B</label>
<coords>0.30519733426244644 0.9510565162951535 -0.5062278801751902</coords>
</point>
<point>
<label>C</label>
<coords>-0.8128366544874484 0.5877852522924732 -0.5062278801751902</coords>
</point>
<point>
<label>F</label>
<coords>-0.003819660112501057 0.0 1.126765281680262</coords>
</point>
<point>
<label>D</label>
<coords>-0.8128366544874485 -0.587785252292473 -0.5062278801751902</coords>
</point>
<point>
<label>E</label>
<coords>0.3051973342624462 -0.9510565162951536 -0.5062278801751902</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.5328608041697043 -0.3348186344436886 -0.4134665796294599 0.6580282918981487</attitude>
</camera>
</figure>
</figures>
<answer>
<type>conditionPlane</type>
<condition/>
<condition>
<type>volumeCutInRatio</type>
<figureName>Pyramid</figureName>
<value>3.398771123309213</value>
</condition>
<condition/>
</answer>
</problem>
<log>
<action>
<className>GVolumeAction</className>
<figureName>Cube</figureName>
<variableName>CubeVolume</variableName>
</action>
<action>
<className>GVolumeAction</className>
<figureName>Pyramid</figureName>
<variableName>PyramidVolume</variableName>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>Ratio</variableName>
<expression>(CubeVolume/PyramidVolume)^(1/3)</expression>
</action>
<action>
<className>GDivideLineAction</className>
<figureName>Pyramid</figureName>
<numerator>Ratio</numerator>
<denominator>1-Ratio</denominator>
<p1Label>F</p1Label>
<p2Label>E</p2Label>
</action>
<action>
<className>GDivideLineAction</className>
<figureName>Pyramid</figureName>
<numerator>Ratio</numerator>
<denominator>1-Ratio</denominator>
<p1Label>F</p1Label>
<p2Label>A</p2Label>
</action>
<action>
<className>GDivideLineAction</className>
<figureName>Pyramid</figureName>
<numerator>Ratio</numerator>
<denominator>1-Ratio</denominator>
<p1Label>F</p1Label>
<p2Label>B</p2Label>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>G,H,I</value>
<figureName>Pyramid</figureName>
</action>
</log>
</solution>