Mid-Arc Triangle

Author

Eric W. Weisstein
November 8, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Mid-ArcTriangle.nb.

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

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

Figure

t=Triangle[{{0,0},{1,0},{.3,.7}}];
Show[Graphics[{
t,
{DarkGreen,
VertexArcs[t,.1],
EqualAngleDivisionTicks[t,2,.1,.02,.07]
},
{Blue,Incircle[t],
Dashing[{.02}],
AngleBisectors[t]
},
{Red,
mt=MidArcTriangle[t]
},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[mt],{"A'","B'","C'"}}],
{
{Incenter[t],"I",Blue}
}
],LabelOffset->.03,PointSize[.025]]

}],AspectRatio->Automatic,PlotRange->All]

Similarity

SimilarQ[t,mt]

Trilinear Vertex Matrix

Trilinears[MidArcTriangle]//MatrixForm//TraditionalForm

Side Lengths

SideLengths[MidArcTriangle]

Area

Simplify[Area[MidArcTriangle] Δ/Area[]]

Centers

(pts={#,KimberlingLookup[#[MidArcTriangle]]}&/@Take[KimberlingCenters,100]);//Timing

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