Nine-Point Conic

Author

Eric W. Weisstein
October 18, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Nine-PointConic.nb.

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

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

Figure

q=Quadrilateral[{{0,0},{1,0},{.7,.5},{.3,.7}}];
m=Midpoint/@CompleteQuadrilateral[q];
eqn=Conic[Coordinates/@Most[m],{x,y}];

<<Graphics`ImplicitPlot`

Show[Graphics[{
CompleteQuadrilateral[q],
{Dashing[{.02}],Sides[q,2.5]},
ImplicitPlot[eqn==0,{x,-2,2},
PlotPoints->100,PlotStyle->Red,DisplayFunction->Identity][[1]],
PointLabels[Join[
Transpose[{VertexPoints[q],{"A","B","C","D"}}],
Append[#,{Blue,LabelOffset->{.06,0}}]&/@Transpose[{DiagonalPoints[q],{"P","Q","R"}}],
Append[#,{Red,LabelOffset->{0,-.07}}]&/@Transpose[{Midpoint/@CompleteQuadrilateral[q],{"(Subscript[M, AB])","(Subscript[M, BC])","(Subscript[M, CD])","(Subscript[M, AD])","(Subscript[M, AC])","(Subscript[M, BD])"}}]
],
LabelOffset->.04
]
}],AspectRatio->Automatic,PlotRange->{{-.2,2.},{-.2,1.2}}]