Yff Contact Circle

Author

Eric W. Weisstein
January 18, 2005

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{3/10,5/10}}]//N[#,10]&;
Show[Graphics[
{
{Purple,Sides[t,2]},
t,
{Blue,YffContactTriangle[t]},
{Red,YffContactCircle[t]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[YffContactTriangle[t]],{"(Subscript[X, A])","(Subscript[X, B])","(Subscript[X, C])"}}],
{
{Center[YffContactCircle[t]],"(Subscript[O, X])",Red}
}
],LabelOffset->.06,PointSize[.025]]
}
],AspectRatio->Automatic,PlotRange->{{-.2,2.4},{-.2,2.1}}]

Center

Center[YffContactCircle][[1]]//TraditionalForm

Radius

CircleRadius[YffContactCircle]//TraditionalForm

Circle Function

CircleFunction[YffContactCircle]//TraditionalForm

IncidentCenters[KimberlingCenters,CyclicTrilinears[CircleFunction[YffContactCircle]]]//Timing

Incident Centers

IncidentCenters[KimberlingCenters,YffContactCircle]//Timing

Derivation

circ=Circumcircle[YffContactTriangle];

Symmetrize[ToSidelengths[Center[circ][[1]]]]

FullSimplify[Factor[Together//@ToSidelengths[CircleRadius[circ]^2]],TriangleQ[]]