File:Musselman theorem.svg

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Summary

Description
English: Musselman theorem schema
Date
Source Own work
Author Claudio Rocchini

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Source Code

Carmetal source:

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<Point name="A" n="0" type="thick" showname="true" x="-0.9155313351498631" y="1.4532243415077204" shape="circle">Punto</Point>
<Point name="B" n="1" type="thick" showname="true" x="4.3451407811080855" y="-1.569482288828338" shape="circle">Punto</Point>
<Point name="C" n="2" type="thick" showname="true" x="-3.58219800181653" y="-1.5549500454132605" shape="circle">Punto</Point>
<Segment name="s1" n="5" color="1" type="thick" from="A" to="B">Segmento da A a B</Segment>
<Segment name="s2" n="8" color="1" type="thick" from="B" to="C">Segmento da B a C</Segment>
<Segment name="s3" n="11" color="1" type="thick" from="C" to="A">Segmento da C a A</Segment>
<Point name="P3" n="1897" color="2" hidden="super" x="x(A)" actx="-0.9155313351498631" y="y(A)" acty="1.4532243415077204" shape="circle" fixed="true">Punto</Point>
<PointOn name="P1" n="1898" color="2" hidden="super" on="s2" alpha="9.884663042646986" x="-74.013931913009" y="-1.4258359594165722" shape="circle">Punto su un oggetto</PointOn>
<Plumb name="p1" n="1899" color="3" hidden="super" point="P3" line="s2" valid="true">Retta perpendicolare per P3 a s2</Plumb>
<Circle name="c1" n="1900" color="4" hidden="super" through="P3" midpoint="P1" acute="true">Circonferenza di centro P1 per P3</Circle>
<Intersection name="A*" n="1901" color="2" showname="true" first="p1" second="c1" awayfrom="P3" shape="circle" which="second">Intersezione tra p1 e c1</Intersection>
<Point name="P4" n="3181" color="2" hidden="super" x="x(B)" actx="4.3451407811080855" y="y(B)" acty="-1.569482288828338" shape="circle" fixed="true">Punto</Point>
<PointOn name="P5" n="3182" color="2" hidden="super" on="s3" alpha="9.884663042646986" x="22.776903445242098" y="28.179840142821813" shape="circle">Punto su un oggetto</PointOn>
<Plumb name="p2" n="3183" color="3" hidden="super" point="P4" line="s3" valid="true">Retta perpendicolare per P4 a s3</Plumb>
<Circle name="c2" n="3184" color="4" hidden="super" through="P4" midpoint="P5" acute="true">Circonferenza di centro P5 per P4</Circle>
<Intersection name="B*" n="3185" color="2" showname="true" first="p2" second="c2" awayfrom="P4" shape="circle" which="second">Intersezione tra p2 e c2</Intersection>
<Point name="P7" n="3950" color="2" hidden="super" x="x(C)" actx="-3.58219800181653" y="y(C)" acty="-1.5549500454132605" shape="circle" fixed="true">Punto</Point>
<PointOn name="P8" n="3951" color="2" hidden="super" on="s1" alpha="9.884663042646986" x="51.08443991190859" y="-28.425212176139123" shape="circle">Punto su un oggetto</PointOn>
<Plumb name="p3" n="3952" color="3" hidden="super" point="P7" line="s1" valid="true">Retta perpendicolare per P7 a s1</Plumb>
<Circle name="c3" n="3953" color="4" hidden="super" through="P7" midpoint="P8" acute="true">Circonferenza di centro P8 per P7</Circle>
<Intersection name="C*" n="3954" color="2" showname="true" first="p3" second="c3" awayfrom="P7" shape="circle" which="second">Intersezione tra p3 e c3</Intersection>
<Segment name="s4" n="3957" color="2" from="B*" to="C*">Segmento da P6 a P9</Segment>
<Segment name="s5" n="3960" color="2" from="C*" to="A*">Segmento da P9 a P2</Segment>
<Segment name="s6" n="3963" color="2" from="A*" to="B*">Segmento da P2 a P6</Segment>
<Midpoint name="P2" n="3966" color="2" type="thin" hidden="true" first="A" second="C" shape="circle">Punto medio tra A e C</Midpoint>
<Midpoint name="P6" n="3969" color="2" type="thin" hidden="true" first="A" second="B" shape="circle">Punto medio tra A e B</Midpoint>
<Plumb name="p4" n="3972" color="2" type="thin" hidden="true" point="P2" line="s3" valid="true">Retta perpendicolare per P2 a s3</Plumb>
<Plumb name="p5" n="3975" color="2" type="thin" hidden="true" point="P6" line="s1" valid="true">Retta perpendicolare per P6 a s1</Plumb>
<Intersection name="O" n="3976" type="thick" showname="true" first="p5" second="p4" shape="circle">Intersezione tra p5 e p4</Intersection>
<Circle name="c4" n="3979" color="4" through="A" midpoint="O" acute="true">Circonferenza di centro P9 per A</Circle>
<Point name="P9" n="4154" color="2" hidden="true" x="(x(A)^2*y(&quot;A*&quot;)-x(A)^2*y(O)+y(&quot;A*&quot;)^2*y(O)-y(&quot;A*&quot;)^2*y(A)-y(&quot;A*&quot;)*y(O)^2+y(&quot;A*&quot;)*y(A)^2-y(&quot;A*&quot;)*x(O)^2+y(O)^2*y(A)-y(O)*y(A)^2+y(O)*x(&quot;A*&quot;)^2+y(A)*x(O)^2-y(A)*x(&quot;A*&quot;)^2)/(2*x(A)*y(&quot;A*&quot;)+(-(2*x(A)))*y(O)+(-(2*y(&quot;A*&quot;)))*x(O)+2*y(O)*x(&quot;A*&quot;)+2*y(A)*x(O)+(-(2*y(A)))*x(&quot;A*&quot;))" actx="-3.4972363615066753" y="(-x(A)^2*x(&quot;A*&quot;)+x(A)^2*x(O)+x(A)*x(&quot;A*&quot;)^2-x(A)*x(O)^2+x(A)*y(&quot;A*&quot;)^2-x(A)*y(O)^2-x(&quot;A*&quot;)^2*x(O)+x(&quot;A*&quot;)*x(O)^2+x(&quot;A*&quot;)*y(O)^2-x(&quot;A*&quot;)*y(A)^2-x(O)*y(&quot;A*&quot;)^2+x(O)*y(A)^2)/(2*x(A)*y(&quot;A*&quot;)+(-(2*x(A)))*y(O)+2*x(&quot;A*&quot;)*y(O)+(-(2*x(&quot;A*&quot;)))*y(A)+(-(2*x(O)))*y(&quot;A*&quot;)+2*x(O)*y(A))" acty="-1.5551057954412082" shape="circle" fixed="true">Point à &quot;(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))&quot;, &quot;(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))&quot; </Point>
<Circle name="c5" n="4155" color="3" large="true" through="A" midpoint="P9">Cercle de centre P10 passant par P7 </Circle>
<Point name="P10" n="4276" color="2" hidden="true" x="(x(&quot;B*&quot;)^2*y(B)-x(&quot;B*&quot;)^2*y(O)+y(B)^2*y(O)-y(B)^2*y(&quot;B*&quot;)-y(B)*y(O)^2+y(B)*y(&quot;B*&quot;)^2-y(B)*x(O)^2+y(O)^2*y(&quot;B*&quot;)-y(O)*y(&quot;B*&quot;)^2+y(O)*x(B)^2+y(&quot;B*&quot;)*x(O)^2-y(&quot;B*&quot;)*x(B)^2)/(2*x(&quot;B*&quot;)*y(B)+(-(2*x(&quot;B*&quot;)))*y(O)+(-(2*y(B)))*x(O)+2*y(O)*x(B)+2*y(&quot;B*&quot;)*x(O)+(-(2*y(&quot;B*&quot;)))*x(B))" actx="1.1773058131869387" y="(-x(&quot;B*&quot;)^2*x(B)+x(&quot;B*&quot;)^2*x(O)+x(&quot;B*&quot;)*x(B)^2-x(&quot;B*&quot;)*x(O)^2+x(&quot;B*&quot;)*y(B)^2-x(&quot;B*&quot;)*y(O)^2-x(B)^2*x(O)+x(B)*x(O)^2+x(B)*y(O)^2-x(B)*y(&quot;B*&quot;)^2-x(O)*y(B)^2+x(O)*y(&quot;B*&quot;)^2)/(2*x(&quot;B*&quot;)*y(B)+(-(2*x(&quot;B*&quot;)))*y(O)+2*x(B)*y(O)+(-(2*x(B)))*y(&quot;B*&quot;)+(-(2*x(O)))*y(B)+2*x(O)*y(&quot;B*&quot;))" acty="3.8140815061165614" shape="circle" fixed="true">Point à &quot;(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))&quot;, &quot;(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))&quot; </Point>
<Circle name="c6" n="4277" color="3" large="true" through="B*" midpoint="P10">Cercle de centre P10 passant par P7 </Circle>
<Point name="P11" n="4404" color="2" hidden="true" x="(x(&quot;C*&quot;)^2*y(C)-x(&quot;C*&quot;)^2*y(O)+y(C)^2*y(O)-y(C)^2*y(&quot;C*&quot;)-y(C)*y(O)^2+y(C)*y(&quot;C*&quot;)^2-y(C)*x(O)^2+y(O)^2*y(&quot;C*&quot;)-y(O)*y(&quot;C*&quot;)^2+y(O)*x(C)^2+y(&quot;C*&quot;)*x(O)^2-y(&quot;C*&quot;)*x(C)^2)/(2*x(&quot;C*&quot;)*y(C)+(-(2*x(&quot;C*&quot;)))*y(O)+(-(2*y(C)))*x(O)+2*y(O)*x(C)+2*y(&quot;C*&quot;)*x(O)+(-(2*y(&quot;C*&quot;)))*x(C))" actx="-0.8905896267644544" y="(-x(&quot;C*&quot;)^2*x(C)+x(&quot;C*&quot;)^2*x(O)+x(&quot;C*&quot;)*x(C)^2-x(&quot;C*&quot;)*x(O)^2+x(&quot;C*&quot;)*y(C)^2-x(&quot;C*&quot;)*y(O)^2-x(C)^2*x(O)+x(C)*x(O)^2+x(C)*y(O)^2-x(C)*y(&quot;C*&quot;)^2-x(O)*y(C)^2+x(O)*y(&quot;C*&quot;)^2)/(2*x(&quot;C*&quot;)*y(C)+(-(2*x(&quot;C*&quot;)))*y(O)+2*x(C)*y(O)+(-(2*x(C)))*y(&quot;C*&quot;)+(-(2*x(O)))*y(C)+2*x(O)*y(&quot;C*&quot;))" acty="1.438893194148125" shape="circle" fixed="true">Point à &quot;(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))&quot;, &quot;(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))&quot; </Point>
<Circle name="c7" n="4405" color="3" large="true" through="C*" midpoint="P11">Cercle de centre P10 passant par P7 </Circle>
<Intersection name="M" n="4406" color="5" type="thick" showname="true" first="c5" second="c6" shape="circle" which="second">Intersezione tra c5 e c6</Intersection>
</Objects>
</Construction>
</CaR>

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23 September 2015

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Date/TimeThumbnailDimensionsUserComment
current13:11, 23 September 2015Thumbnail for version as of 13:11, 23 September 2015673 × 478 (13 KB)RocchiniUser created page with UploadWizard

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