Journal for Geometry and Graphics, Vol. 1, No. 2, pp. 119 - 133 (1997)

Affine and Projective Generalization of Wallace Lines

Oswald Giering

Center of Mathematical Sciences, Munich University of Technology,
Arcisstr. 21, D-80290 München, Germany

Abstract: 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.

Keywords: Wallace line, geometry of the triangle, collinear points

Classification (MSC2000): 51M05; 51N10

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