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AdamsCircumference::usage="It is the circle that has the center to the incenter. To obtain ii first we will calculate the tangent points of the inscribed circumference and we will trace the Gergonne triangle which is what passes through those points. Then we will get the Gergonne point of the base triangle. By the Gergonne point we draw a parallel line to one side of the Gergonne triangle and we will obtain one of the points through which the Adams circumference passes. We will calculate the radius at that point and the center. References: Math World: Adams Circle; Personal. ";AdamsCircumference[tri={{x1_,y1_},{x2_,y2_},{x3_,y3_}}]:=Module{},DEP=Det[{{x1,y1,1},{x2,y2,1},{x3,y3,1}}];IfDEP==0,Print[PasteButton["The points do not form a triangle"]],η=TriangleCenter[tri,"Incenter"];cx=η[[1]];cy=η[[2]];η1=TriangleMeasurement[tri,"Inradius"];ri=η1;s1=Solve[{(y1-y2)x+(x2-x1)y+(x1y2-y1x2)==0,+==},{x,y}];xt11=x/.Take[s1,{1}];xt1=xt11.{1};yt11=y/.Take[s1,{1}];yt1=yt11.{1};s2=Solve[{(y2-y3)x+(x3-x2)y+(x2y3-y2x3)==0,+==},{x,y}];xt22=x/.Take[s2,{1}];xt2=xt22.{1};yt22=y/.Take[s2,{1}];yt2=yt22.{1};s3=Solve[{(y1-y3)x+(x3-x1)y+(x1y3-y1x3)==0,+==},{x,y}];xt33=x/.Take[s3,{1}];xt3=xt33.{1};yt33=y/.Take[s3,{1}];yt3=yt33.{1};s4=Solve[{(x1-xt2)y-(y1-yt2)x-y1(x1-xt2)+x1(y1-yt2)==0,(x2-xt3)y-(y2-yt3)x-y2(x2-xt3)+x2(y2-yt3)==0},{x,y}];xg1=x/.s4;xg=xg1.{1};yg1=y/.s4;yg=yg1.{1};s5=Solve[{(yt2-yt3)x+(xt3-xt2)y-xt3yg+xt2yg+xgyt3-xgyt2==0,(y2-y3)x+(x3-x2)y+(x2y3-y2x3)==0},{x,y}];xc22=x/.s5;xc2=xc22.{1};yc22=y/.s5;yc2=yc22.{1};r=+;r1=N[r];g1=Line[{{x1,y1},{x2,y2},{x3,y3},{x1,y1}}];g2=Point[{xg,yg}];g3=Point[{cx,cy}];g4=Point[{xt1,yt1}];g5=Point[{xc2,yc2}];g6=Point[{xt2,yt2}];g7=Point[{xt3,yt3}];g8=Line[{{xt1,yt1},{xt2,yt2},{xt3,yt3},{xt1,yt1}}];g9=InfiniteLine[{{xg,yg},{xc2,yc2}}];g10=Circle[{cx,cy},r];g11=Point[{x1,y1}];g12=Point[{x2,y2}];g13=Point[{x3,y3}];D1=N[-2cx];E1=N[-2cy];F1=N[+-];Speak["Below is the information about the circumference of Adams"];Print[PasteButton["The equation of Adams circumference:"]];Print[" "];Print[{1,1,D1,E1,F1}.{,,x,y,1}==0];Print[" "];Print[PasteButton["Coordinates of the center and radius:"]];Print[" "];xce=N[cx];yce=N[cy];s=Grid[{{Centro,radio},{{xce,yce},r1}},FrameAll];Print[s];Print[" "];SwatchLegend[{Red,Brown,Green,Black,Purple,DarkYellow},{"Adams circumference and its center","Gergonne's triangle","Tangent points of the inscribed circumference","Parallel line one one side of the Gergonne triangle, that passes theough the Gergonne point","Gergonne point","Intersection point of the straight line that passes through the point of Gergonne with the circumference"}]Show[{Graphics[{Purple,Thick,PointSize[0.018],g2}],Graphics[{Blue,g1}],Graphics[{Red,Thick,PointSize[0.018],g3}],Graphics[{Green,Thick,PointSize[0.018],g4}],Graphics[{DarkYellow,Thick,PointSize[0.018],g5}],Graphics[{Green,Thick,PointSize[0.018],g6}],Graphics[{Green,Thick,PointSize[0.018],g7}],Graphics[{Black,Thick,PointSize[0.018],g11}],Graphics[{Black,Thick,PointSize[0.018],g12}],Graphics[{Black,Thick,PointSize[0.018],g13}],Graphics[{Brown,g8}],Graphics[{Black,Dashed,g9}],Graphics[{Red,g10}]},AxesTrue,AspectRatioAutomatic,AxesOrigin{0,0},ImageSize500,PlotLabelStyle[Framed["Adams Circumference"],16,Blue,BackgroundYellow]]
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In the command below, type the new coordinates of the points. Evaluate the notebook.
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AdamsCircumference[tri={{-2,5},{7,12},{9,-4}}]
21.8942-8.13894x+-9.85016y+0
2
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Centro | radio |
{4.06947,4.92508} | 4.35003 |
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