Geodesic
Affine and Projective Generalization of Wallace Lines
Journal for geometry and graphics, Tome 1 (1997) no. 2, pp. 119-134 Cet article a éte moissonné depuis la source Heldermann Verlag

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If one draws in a plane from a point $X$ the perpendiculars onto the sides $AB,BC,C A$ of a triangle $ABC$ and if the feet of these perpendiculars $P\in AB$, $Q\in BC$, $R\in C A$ lie on a line -- the Wallace line of $X$ -- then $X$ lies on the circumcircle of the triangle $ABC$. We introduce two generalizations: If the affine feet $P, Q, R$ lie on the affine Wallace line of $X$ with respect to a center $Z$ or if the projective feet $P, Q, R$ lie on the projective Wallace line of $X$ with respect to a center $Z$ and an axis $f$ then $X$ lies on a conic. 
@article{JGG_1997_1_2_a2,
     author = {O. Giering},
     title = {Affine and {Projective} {Generalization} of {Wallace} {Lines}},
     journal = {Journal for geometry and graphics},
     pages = {119--134},
     year = {1997},
     volume = {1},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_1997_1_2_a2/}
}
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O. Giering. Affine and Projective Generalization of Wallace Lines. Journal for geometry and graphics, Tome 1 (1997) no. 2, pp. 119-134. http://geodesic.mathdoc.fr/item/JGG_1997_1_2_a2/