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.

EqualCirclesAtVertices.html

Menelaus.html

Produced with EucliDraw© |