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 $GN = 2IG$.
Problem of the day (Day 2)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Problem of the day (Day 2)
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
বড় ভালবাসি তোমায়,মা
Re: Problem of the day (Day 2)
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)
(i have seen this process of pic in other topics but couldn't really understand)
Try not to become a man of success but rather to become a man of value.-Albert Einstein
Re: Problem of the day (Day 2)
This is Nagel point,not negal.photon wrote:i got a proof of $\boxed{negal }$point
One one thing is neutral in the universe, that is $0$.
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Problem of the day (Day 2)
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.
বড় ভালবাসি তোমায়,মা
Re: Problem of the day (Day 2)
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?
Try not to become a man of success but rather to become a man of value.-Albert Einstein