Problem of the day (Day 2)

[Moon]

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 $GN = 2IG$.

[Tahmid Hasan]

let the 3 excircles touch $BC$ at $X$,$AC$ at $Y$ and $AB$ at $Z$.now ceva $\frac{BX.CY.AZ}{CX.AY.BZ}$=$\frac{s-c.s-a.s-b}{s-b.s-c.s-a}$=1.so nagel point exists

[photon]

i got a proof of negal point existence a few weeks ago, not like tahmid's.but to state it i need to draw a picture,but i don't know.....i wish any one will give me proper steps for it
(i have seen this process of pic in other topics but couldn't really understand)

[Masum]

i got a proof of $\boxed{negal }$point

This is Nagel point,not negal.

[Tahmid Hasan]

there is many software for drawing geometric figures,i would recommend cabri.you can download it fro the net.then after making a file jst attach it with the post.

[photon]

i have tried to upload the attachment with geogebra,but when i click "add the file",it comes that The extension ggb is not allowed.what does it mean?i don't get that.....can anybody help?