What is the locus of orange points for which the purple lines are parallel? The fixed cevians of the triangle BCD are angle bisectors.
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The purple lines are parallel.
A Typo: Where it says line F_2’C, that should be line E_2’D. Also, the proof here is for the case in which B and D lie on the same side of the line EC, as shown in the figure. For the case in which B and D lie on opp. sides of line EC, same basic ideas – a very similar proof.