[alogo] Cevians and parallels

Consider a triangle ABC a point G, the Cevians of it, the cevian triangle DEF, the trilinear polar A'B' of G etc.. Then take paralles to the sides of the triangle in respective distances h1, h2, h3. Find a necessary condition for the hi, such that the intersection points {D',E',F'} of these parallels with the sides of DEF are again on a line.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]
[2_0] [2_1] [2_2] [2_3]

After Menelaus a necessary and sufficient condition for the collinearity of {D',E',F'} is (F'D/F'E)*(D'E/D'F)*(E'F/E'D) = 1. Denoting by [D,AB] the distance of point D from line AB this amounts to the condition:


This property is used in EqualCirclesAtVertices.html to prove the perspectivity of two important triangles.

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