<?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 framework is shaped like a regular pyramid. A long cylindric bar is passed through the interior of the framework so that the surface of the bar touches all edges except AB. Locate the point where the bar touches edge DC.</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Pyramid</name>
<color>#ffff</color>
<transparent>true</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>1.0 0.0 -0.5062278801751902</coords>
</point>
<point>
<label>B</label>
<coords>-0.49999999999999967 0.8660254037844386 -0.5062278801751902</coords>
</point>
<point>
<label>C</label>
<coords>-0.5000000000000003 -0.8660254037844386 -0.5062278801751902</coords>
</point>
<point>
<label>D</label>
<coords>0.0 0.0 1.1267652816802618</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.47929167563788255 -0.35430682960110604 -0.46091840333735073 0.6574955403857816</attitude>
</camera>
</figure>
</figures>
<answer>
<type>pointSet</type>
<coords>-0.2771332833038013 -0.4800089271505632 0.221651768564948</coords>
</answer>
</problem>
<log>
<action>
<className>GDrawMidpointAction</className>
<figureName>Pyramid</figureName>
<p1Label>B</p1Label>
<p2Label>A</p2Label>
</action>
<action>
<className>GCutAction</className>
<figureName>Pyramid</figureName>
<p0Label>E</p0Label>
<p1Label>D</p1Label>
<p2Label>C</p2Label>
<figure1Name>Figure1</figure1Name>
<figure2Name>Figure2</figure2Name>
</action>
<action>
<className>GDrawBisectorAction</className>
<figureName>Figure2</figureName>
<p0Label>C</p0Label>
<p1Label>D</p1Label>
<p2Label>E</p2Label>
</action>
<action>
<className>GDrawBisectorAction</className>
<figureName>Figure2</figureName>
<p0Label>D</p0Label>
<p1Label>C</p1Label>
<p2Label>E</p2Label>
</action>
<action>
<className>GIntersectAction</className>
<figureName>Figure2</figureName>
<p11Label>D</p11Label>
<p12Label>G</p12Label>
<p21Label>C</p21Label>
<p22Label>F</p22Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>H</p0Label>
<p1Label>D</p1Label>
<p2Label>C</p2Label>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>I</value>
<figureName>Figure2</figureName>
</action>
</log>
</solution>