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December 19th, 2015, 11:02 AM  #1 
Newbie Joined: Oct 2015 From: Eskişehir Posts: 11 Thanks: 0  The equality on Euler lines? Please help. It is all ok until $GG_1/G_1E=AI/ID$ ???? I have been spending hours to understand it but I couldn't. How can he write this? Please help Last edited by skipjack; December 20th, 2015 at 07:13 PM. 
December 20th, 2015, 07:54 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,918 Thanks: 2201 
$BD = CD$ (as they subtend equal angles at A), so D lies on the perpendicular bisector of $BC$. Hence $O_1$ lies on the line OED, and so equation (2) follows from the fact that $GG_1E\parallel\! AID$. 

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