Gotthard Weise,
Cevian projections of inscribed triangles and generalized Wallace lines,
Forum Geometricorum, 16
(2016) 241--248.
Abstract. Let Delta = ABC be a reference triangle and Delta' = A'B'C' an
inscribed triangle of Delta. We define the cevian projection of Delta'
as the cevian triangle Delta_P of a certain point P. Given a point P
not on a sideline, all inscribed triangles with common cevian projection Delta_P
form a family D_P = {Delta(t) = A_tB_tC_t, t in R}.
The parallels of the lines AA_t, BB_t, CC_t through any point of a certain
circumconic C_P intersect the sidelines a, b, c in collinear points
X, Y, Z, respectively. This is a generalization of the well-known theorem of Wallace.
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