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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a>  implies  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="euclid10.html#K1" title="EUCLID10:func.1">the_diameter_of_the_circumcircle</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>) )</span><br/>





<span class="kw">assume </span><a NAME="E1:16"/>
 <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="euclid10.html#K1" title="EUCLID10:func.1">the_diameter_of_the_circumcircle</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>)</span><br/>

<a NAME="E2:16"/><span class="kw">then </span>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="euclid_6.html#K1" title="EUCLID_6:func.1">the_area_of_polygon3</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid11.html#T10" target="_self" onmouseover="rs('euclid11/T10')" onmouseout="rh()">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="euclid10.html#K1" title="EUCLID10:func.1">the_diameter_of_the_circumcircle</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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