Soddy Triangles

Author

Eric W. Weisstein
March 15, 2004

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{.3,.7}}];
inner=Show[Graphics[{
t,
{Blue,TangentCircles[t]},
{Red,it=InnerSoddyTriangle[t]},
{Orange,InnerSoddyCircle[t]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[it],{"P","Q","R"}}],
{
{InnerSoddyCenter[t],"S",Orange}
}
],PointSize[.022],LabelOffset->.05]
}],AspectRatio->Automatic,PlotRange->{{-.3,1.2},{-.4,.8}}]

t=Triangle[{{0,0},{1,0},{.3,.7}}];
outer=Show[Graphics[{
t,
{Blue,TangentCircles[t]},
{Red,ot=OuterSoddyTriangle[t]},
{Orange,OuterSoddyCircle[t]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[ot],{"P'","Q'","R'"}}],
{
{OuterSoddyCenter[t],"S'",Orange}
}
],PointSize[.022],LabelOffset->.05]
}],AspectRatio->Automatic,PlotRange->{{-.6,1.8},{-1,1.3}}]

Show[GraphicsArray[{inner,outer}]]