In[]:=
AnticomplementaryCircumference::usage=" It is the circumference circumscribed to the anticomplementary triangle. It has its center in the orthocenter of the base triangle and its radius is twice the circumradius of the base triangle. The anticomplementary triangle of the base triangle is that formed by the parallel lines on each side that pass through the opposite vertex. References: Wolfram MathWorld: Anticomplementary Circle, Anticomplementary Triangle; Personal. ";​​​​AnticomplementaryCircumference[tri={{x1_,y1_},{x2_,y2_},{x3_,y3_}}]:=​​Module{},DEP=Det[{{x1,y1,1},{x2,y2,1},{x3,y3,1}}];IfDEP==0,Print[PasteButton["The points do not form a triangle"]],​​η=TriangleMeasurement[tri,"Circumradius"];​​rc=η;​​ξ=TriangleCenter[tri,"Orthocenter"];​​xo=ξ[[1]];​​yo=ξ[[2]];​​​​aa=
2
(x3-x2)
+
2
(y3-y2)
;bb=
2
(x3-x1)
+
2
(y3-y1)
;cc1=
2
(x2-x1)
+
2
(y2-y1)
;​​​​xx=-aabbcc1;yy=aabbcc1;zz=aabbcc1;​​
λ
1
=
xx
xx+yy+zz
;
λ
2
=
yy
xx+yy+zz
;
λ
3
=
zz
xx+yy+zz
;​​XA=
λ
1
{x1,y1}+
λ
2
{x2,y2}+
λ
3
{x3,y3};​​xXA=Take[XA,{1}].{1};yXA=Take[XA,{2}].{1};​​xx1=aabbcc1;yy1=-aabbcc1;zz1=aabbcc1;​​
λ
4
=
xx1
xx1+yy1+zz1
;
λ
5
=
yy1
xx1+yy1+zz1
;
λ
6
=
zz1
xx1+yy1+zz1
;​​XB=
λ
4
{x1,y1}+
λ
5
{x2,y2}+
λ
6
{x3,y3};​​xXB=Take[XB,{1}].{1};yXB=Take[XB,{2}].{1};​​xx2=aabbcc1;yy2=aabbcc1;zz2=-aabbcc1;​​
λ
7
=
xx2
xx2+yy2+zz2
;
λ
8
=
yy2
xx2+yy2+zz2
;
λ
9
=
zz2
xx2+yy2+zz2
;​​XC=
λ
7
{x1,y1}+
λ
8
{x2,y2}+
λ
9
{x3,y3};​​xXC=Take[XC,{1}].{1};yXC=Take[XC,{2}].{1};​​ra=2rc;​​w=Grid[{{AnticomplementaryCenter,AnticomplementaryRadius},{{xo,yo},ra}},ItemSize15,ItemStyle15,FrameAll];​​Print[w];​​Print[" "];​​g1=Line[{{x1,y1},{x2,y2},{x3,y3},{x1,y1}}];​​g2=Line[{{xXA,yXA},{xXB,yXB},{xXC,yXC},{xXA,yXA}}];;​​g3=Point[{x1,y1}];​​g4=Point[{x2,y2}];​​g5=Point[{x3,y3}];​​g6=Point[{xXA,yXA}];​​g7=Point[{xXB,yXB}];​​g8=Point[{xXC,yXC}];​​g9=Circle[{xo,yo},ra];​​g10=Point[{xo,yo}];​​SwatchLegend[{Gray,Brown,Blue},{"Anticomplementary triangle and vertices","Anticomplementary circumference and its center (orthocenter of the base triangle)","Base triangle"}]​​Show[{Graphics[{Blue,g1}],Graphics[{Gray,g2}],Graphics[{Black,Thick,PointSize[0.01],g3}],Graphics[{Black,Thick,PointSize[0.01],g4}],Graphics[{Black,Thick,PointSize[0.01],g5}],Graphics[{Gray,Thick,PointSize[0.01],g6}],Graphics[{Gray,Thick,PointSize[0.01],g7}],Graphics[{Gray,Thick,PointSize[0.01],g8}],​​Graphics[{Brown,Thick,PointSize[0.01],g10}],Graphics[{Brown,g9}]},AxesTrue,AxesOrigin{0,0},AspectRatioAutomatic,ImageSize700,PlotLabelStyle[Framed["The anticomplementary circumference :"],16,Blue,BackgroundYellow]]​​​​​​
In the command below, type the new coordinates of the points. Evaluate the notebook.
In[]:=
AnticomplementaryCircumference[tri={{-2,6},{0,3},{5,2}}]
AnticomplementaryCenter
AnticomplementaryRadius
{-4,-4}
130
Out[]=
Anticomplementary triangle and vertices
Anticomplementary circumference and its center (orthocenter of the base triangle)
Base triangle