Apollonius Point

Author

Eric W. Weisstein
January 29, 2003

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

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

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

Initialization

<<PlaneGeometry`;

Figure

t=Triangle[{{0,0},{1,0},{1/4,.7}}];
n=FullSimplify[NinePointCircle[t]];
j=FullSimplify[Excircles[t]];
v=Point/@Vertices[t];
apt=ApolloniusPoint[t];

Show[Graphics[{
{Dashing[{.02}],Sides[t,1]},
t,
{Blue,j=Excircles[t]},
{Green,ap=ApolloniusOuterCircle[j]},
abc=First/@(Intersections[ap,#]&/@j),
{Red,Line/@Transpose[{Vertices[t],Coordinates/@abc}]},
PointLabels[Join[
Transpose[{v,{"A","B","C"}}],
Append[#,Blue]&/@Transpose[{abc,{"A'","B'","C'"}}],
{{apt,"Ap",Red}}
]
]
},AspectRatio->Automatic],
ImageSize->250
]