<?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>An ant is crawling on the surface of this regular pyramid. It starts at a vertex on the base, goes up to the nearest point on the next edge, then  to the nearest point on the next edge, and so on, until it reaches again the edge it started at. How far will be the ant from the nearest edge on the base of the pyramid?</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Pyramid</name>
<color>#9900</color>
<transparent>true</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>1.01 0.0 -0.5062278801751902</coords>
</point>
<point>
<label>B</label>
<coords>0.5100000000000001 0.8660254037844386 -0.5062278801751902</coords>
</point>
<point>
<label>C</label>
<coords>-0.48999999999999977 0.8660254037844387 -0.5062278801751902</coords>
</point>
<point>
<label>G</label>
<coords>0.01000000000000005 0.0 1.126765281680262</coords>
</point>
<point>
<label>D</label>
<coords>-0.99 0.0 -0.5062278801751902</coords>
</point>
<point>
<label>E</label>
<coords>-0.49000000000000044 -0.8660254037844385 -0.5062278801751902</coords>
</point>
<point>
<label>F</label>
<coords>0.5099999999999993 -0.866025403784439 -0.5062278801751902</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.5305143042165645 -0.2839146482822148 -0.3870482598302519 0.6986706592342166</attitude>
</camera>
</figure>
</figures>
<answer>
<type>number</type>
<value>1.0814378294330151</value>
</answer>
</problem>
<log>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>E</p0Label>
<p1Label>F</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>H</p0Label>
<p1Label>G</p1Label>
<p2Label>A</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>I</p0Label>
<p1Label>G</p1Label>
<p2Label>B</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>J</p0Label>
<p1Label>C</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>K</p0Label>
<p1Label>G</p1Label>
<p2Label>D</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>L</p0Label>
<p1Label>E</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Pyramid</figureName>
<p0Label>M</p0Label>
<p1Label>F</p1Label>
<p2Label>E</p2Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Pyramid</figureName>
<p1Label>M</p1Label>
<p2Label>N</p2Label>
<variableName>Distance</variableName>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>Distance</value>
</action>
</log>
</solution>