Every inscribed in a triangle ABC conic (e) is the envelope of the tripolars E

[1] Apply Pascal's theorem (for quadrangles) to quadrangle ED

[2] Apply Brianchon's theorem (for quadrangles) to quadrangle ABGE

[3] By considering the pole-polar relation for points H and E

[4] Let J be the intersection point of D

[5] By [1] (E

[6] By the aforementioned discussion A' is on the tripolar of D.

There are several other relations of coincidence and harmonicity of tetrads of points hidden in this figure. For example, points {K,L,E

HyperbolaPropertyParallels2.html

InconicsTangents.html

PascalOnQuadrangles.html

TrilinearPolar.html

Trilinears.html

Produced with EucliDraw© |