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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th17</font></span>: <a NAME="T22"><span class="comment"><font color="firebrick">:: EUCLID11:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font>, <font color="Olive" title="b4">E</font>, <font color="Olive" title="b5">F</font>, <font color="Olive" title="b6">G</font> being   <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>  st <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="euclid_6.html#NR1" title="EUCLID_6:NR.1">is_a_triangle</a>  &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</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>  &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b4">E</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b4">E</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b5">F</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b5">F</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b6">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 &amp;  <a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b6">G</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K4" title="EUCLID_3:func.4">angle</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>)</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 holds <br/>( <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">F</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">E</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b6">G</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">F</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> &amp; <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">F</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">E</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">E</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b6">G</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> &amp; <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b6">G</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">F</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">E</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b6">G</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> )</div></div>
