Problem of the day (Day 2)
Posted: Thu Feb 17, 2011 5:12 pm
First, I think some of you may know this property already. If you don't know, try this cool one!
(Nagel line) Let $ABC$ be a triangle. Let the excircle of $ABC$ opposite to $A$ touch side $BC$ at $D$. Similarly define $E$ on $AC$ and $F$ on $AB$. Then $AD, BE, CF$ concur (why?) at a point $N$ known
as the Nagel point.
Let $G$ be the centroid of $ABC$ and $I$ the incenter of $ABC$. Show that $I, G, N$ lie in that order on a line (known as the Nagel line) and $GN = 2IG$.
(Nagel line) Let $ABC$ be a triangle. Let the excircle of $ABC$ opposite to $A$ touch side $BC$ at $D$. Similarly define $E$ on $AC$ and $F$ on $AB$. Then $AD, BE, CF$ concur (why?) at a point $N$ known
as the Nagel point.
Let $G$ be the centroid of $ABC$ and $I$ the incenter of $ABC$. Show that $I, G, N$ lie in that order on a line (known as the Nagel line) and $GN = 2IG$.