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triangle inequality
Lonesan   5
N Mar 4, 2016 by Lonesan
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In any triangle is true:


$\frac{l_al_bl_c}{h_ah_bh_c} = \frac{8R^2}{s^2+2Rr+r^2 } \ge 1 \ \ ; $


Greetings! :-)
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Lonesan
Feb 28, 2016
Lonesan
Mar 4, 2016
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Lonesan
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Lonesan
#1 h  Feb 28, 2016, 7:14 PM • 2 Y
Y by Adventure10, Mango247

In any triangle is true:


$\frac{l_al_bl_c}{h_ah_bh_c} = \frac{8R^2}{s^2+2Rr+r^2 } \ge 1 \ \ ; $


Greetings! :-)
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ahmedosama
104 posts
ahmedosama
#2 h  Feb 29, 2016, 6:46 PM • 2 Y
Y by Adventure10, Mango247
What is $l$
$h$ ????
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arqady
30154 posts
arqady
#3 h  Feb 29, 2016, 7:17 PM • 2 Y
Y by Adventure10, Mango247
Lonesan wrote:
In any triangle is true:


$\frac{l_al_bl_c}{h_ah_bh_c} = \frac{8R^2}{s^2+2Rr+r^2 } \ge 1 \ \ ; $
What do you wish to say, dear Lonesan? :maybe:
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Lonesan
2170 posts
Lonesan
#4 h  Feb 29, 2016, 11:36 PM • 2 Y
Y by Adventure10, Mango247
ahmedosama wrote:
What is $l$
$h$ ????
arqady wrote:
Lonesan wrote:
In any triangle is true:


$\frac{l_al_bl_c}{h_ah_bh_c} = \frac{8R^2}{s^2+2Rr+r^2 } \ge 1 \ \ ; $
What do you wish to say, dear Lonesan? :maybe:

We use for bisectors $l_a, l_b, l_c$, instead of $w_a, w_b, w_c$. I am sorry I didn't realize that when I wrote the problem!
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Virgil Nicula
7054 posts
Virgil Nicula
#5 h  Mar 4, 2016, 12:09 PM • 2 Y
Y by Bottp, Adventure10
See the proposed problem PP3 (first identity and second inequality) here
This post has been edited 3 times. Last edited by Virgil Nicula, Mar 4, 2016, 1:39 PM
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Lonesan
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Lonesan
#6 h  Mar 4, 2016, 4:29 PM • 2 Y
Y by Adventure10, Mango247
Virgil Nicula wrote:
See the proposed problem PP3 (first identity and second inequality) here

Thank you nea Virgile! What is true - is true! I hope at least they will follow the link and read your solution. Greetings! :-)
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