Anticenter

Author

Eric W. Weisstein
April 18, 2004

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

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

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

Diagram

AnticenterDiagram[q_List]:=Module[{},
quad=Quadrilateral[{Cos[#],Sin[#]}&/@q];
m[i_]:=Midpoints[quad][[i]];
ma[i_]:=Foot[Maltitudes[quad][[i]]];
v[i_]:=Vertices[quad][[i]];

pts={v[1],"A",v[2],"B",v[3],"C",v[4],"D"};
redpts={
m[1],"(Subscript[M, AB])",m[2],"(Subscript[M, BC])",m[3],"(Subscript[M, CD])",m[4],"(Subscript[M, AD])",
ma[1],"(Subscript[F, CD])",ma[2],"(Subscript[F, AD])",ma[3],"(Subscript[F, AB])",ma[4],"(Subscript[F, BC])"
};
bluepts={Centroid,"G",{0,0},"O",Anticenter,"T"};
{
quad,
PointLabels[quad,pts,.04,{-.04,-.09}],
{
Red,
Maltitudes[quad],
PointLabels[quad,redpts,.04,{-.04,-.09}]
},
Circle[{0,0},1],
{
Blue,
PointLabels[quad,bluepts,.04,{-.04,-.09}],
Line[{{0,0},Coordinates@Anticenter[quad]}]
}
}
]

Show[Graphics[AnticenterDiagram[{.1,1.,2.7,4.3}]],AspectRatio->Automatic]