Circumtangential Triangle

Author

Eric W. Weisstein
November 8, 2005

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

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

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

Equilateral

EquilateralQ[CircumtangentialTriangle[RandomTriangle[20]]]

Simplify[#^2&/@EquilateralQ[CircumtangentialTriangle]/.C->π-A-B]

Figure

t=Triangle[{{0,0},{1,0},{.1,.7}}];
ct=CircumtangentialTriangle[t];
Show[Graphics[{
t,
{Blue,Circumcircle[t]},
{Red,ct,VertexArcs[ct,.15],EqualAngleTicks[ct,1,.15,.05]},
{DarkGreen,TangentialTriangle[ct]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[ct],{"A'","B'","C'"}}]
],LabelOffset->.06,PointSize[.03]]
}],AspectRatio->Automatic,ImageSize->200]

SideLengths[Evaluate[ct]]

Trilinear Vertex Matrix

Trilinears[CircumtangentialTriangle]//MatrixForm//TraditionalForm

Area

Area[CircumnormalTriangle]

Centers

(pts={#,KimberlingLookup[#[CircumtangentialTriangle]]}&/@Take[KimberlingCenters,10]);//Timing

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