Third Morley Adjunct Triangle

Author

Eric W. Weisstein
November 15, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/ThirdMorleyAdjunctTriangle.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ThirdMorleyAdjunctTriangle.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Morley Triangle and Adjunct

Figure

t=Triangle[{{0,0},{1,0},{.3,.7}}];
Show[Graphics[{
t,
{Blue,
Rest/@MapIndexed[RotateLeft[#1,#2+2]&,Cevians[t,#]&/@VertexPoints[MorleyTriangle[3][t]]]
},
{DarkGreen,
VertexArcs[t,.1],
EqualAngleDivisionTicks[t,3,.1,.02,.07]
},
{Red,mt=MorleyTriangle[3][t]},
{DarkOrange,mat=MorleyAdjunctTriangle[3][t]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[mt],{"A'","B'","C'"}}],
Append[#,DarkOrange]&/@Transpose[{VertexPoints[mat],{"A''","B''","C''"}}]
],LabelOffset->.03]
}],AspectRatio->Automatic,PlotRange->All]

Trilinear Vertex Matrix

TrilinearVertexMatrix[MorleyAdjunctTriangle[3]]//MatrixForm//TraditionalForm

Sides

Area

Perspectors

tris=DeleteCases[Triangles,MorleyAdjunctTriangle[3]];

pts=DeleteCases[{#,k=KimberlingLookup[Perspector[MorleyAdjunctTriangle[3],#]]}&/@Take[tris,All],_?(Last[#]==={}&)]

{Name[#[[1]]],X[#[[2,1]]],Name[X[#[[2,1]]]]}&/@Cases[pts,_?(Last[#]=!={}&)]//TableForm

Centers

(pts={#,KimberlingLookup[#[MorleyAdjunctTriangle[2]]]}&/@Take[KimberlingCenters,All]);//Timing

{#[[1]],Name[#[[1]]],X[#[[2,1]]],Name[X[#[[2,1]]]]}&/@Cases[pts,_?(Last[#]=!={}&)]//TableForm