Denote by d=|AB|. Then (x/y):(d/z) is the cross ratio of the four points {A,D,F,B} measured on line AB, and this is independent of the position of P. Obviously the property extends to chords of conics. The reduction of the property to the cross ratio of four points on a conic is due to Bankoff.

Chasles_Steiner_Envelope.html

Complex_Cross_Ratio.html

Complex_Cross_Ratio2.html

CrossRatio0.html

CrossRatioLines.html

FourTangentsCrossRatio.html GoodParametrization.html

Harmonic.html

Harmonic_Bundle.html

HarmonicQuad.html

HomographicRelation.html

HomographicRelationExample.html

ParabolaProperty.html

RectHypeRelation.html

Produced with EucliDraw© |