Kosnita Theorem

Author

Eric W. Weisstein
April 18, 2003

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

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

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

Initialization

<<PlaneGeometry`

Figure

t=Triangle[{{0,0},{1,0},{.3,.7}}];
o=Triangle/@(FlattenAt[#,1]&/@(Coordinates/@{#,Circumcenter[t]}&/@Sides[t]));
Show[Graphics[{
t,
{Blue,
Circumcircle/@o
},
{Red,
Line/@Transpose[{Coordinates/@Circumcenter/@o,Vertices[t]}]
},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
Append[#,Blue]&/@Transpose[{Circumcenter/@o,{"(Subscript[O, BCO])","(Subscript[O, CAO])","(Subscript[O, ABO])"}}],
{
{Circumcenter[t],"O",Blue},
{X[54][t],"Ko",Red}
}
],
{PointSize[.025],LabelOffset->.06}
]
}],AspectRatio->Automatic]