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Question-168606




Question Number 168606 by Shrinava last updated on 14/Apr/22
Commented by mr W last updated on 14/Apr/22
[ABC]=area of ΔABC?  is I_a  opposite to A?
$$\left[{ABC}\right]={area}\:{of}\:\Delta{ABC}? \\ $$$${is}\:{I}_{{a}} \:{opposite}\:{to}\:{A}? \\ $$
Commented by Shrinava last updated on 14/Apr/22
Sorry-sorry sir, M,L,L no  M,L,K
$$\mathrm{Sorry}-\mathrm{sorry}\:\boldsymbol{\mathrm{sir}},\:\mathrm{M},\mathrm{L},\mathrm{L}\:\mathrm{no}\:\:\mathrm{M},\mathrm{L},\mathrm{K} \\ $$
Commented by mr W last updated on 14/Apr/22
you mean M,L,K, not M,L,L. this is  clear.  please answer my questions above!
$${you}\:{mean}\:{M},{L},{K},\:{not}\:{M},{L},{L}.\:{this}\:{is} \\ $$$${clear}. \\ $$$${please}\:{answer}\:{my}\:{questions}\:{above}! \\ $$
Commented by Shrinava last updated on 14/Apr/22
Yes sir
$$\boldsymbol{\mathrm{Yes}}\:\boldsymbol{\mathrm{sir}} \\ $$
Commented by Shrinava last updated on 14/Apr/22
Sir, I would like to see your perfect solution
$$\boldsymbol{\mathrm{Sir}},\:\mathrm{I}\:\mathrm{would}\:\mathrm{like}\:\mathrm{to}\:\mathrm{see}\:\mathrm{your}\:\mathrm{perfect}\:\mathrm{solution} \\ $$
Commented by mr W last updated on 22/Apr/22
i have proved both statements.  in AB+BC+CA≤2(ML+LK+KM)  “=” is never valid. In fact we have  AB+BC+CA<(4/3)(ML+LK+KM)
$${i}\:{have}\:{proved}\:{both}\:{statements}. \\ $$$${in}\:{AB}+{BC}+{CA}\leqslant\mathrm{2}\left({ML}+{LK}+{KM}\right) \\ $$$$“=''\:{is}\:{never}\:{valid}.\:{In}\:{fact}\:{we}\:{have} \\ $$$${AB}+{BC}+{CA}<\frac{\mathrm{4}}{\mathrm{3}}\left({ML}+{LK}+{KM}\right) \\ $$
Answered by mr W last updated on 15/Apr/22
Commented by Shrinava last updated on 15/Apr/22
Sir, the start is perfect (as usual)
$$\boldsymbol{\mathrm{Sir}},\:\mathrm{the}\:\mathrm{start}\:\mathrm{is}\:\mathrm{perfect}\:\left(\mathrm{as}\:\mathrm{usual}\right) \\ $$
Commented by Shrinava last updated on 15/Apr/22
Sir, if possible, you would note the  continuation...
$$\boldsymbol{\mathrm{Sir}},\:\mathrm{if}\:\mathrm{possible},\:\mathrm{you}\:\mathrm{would}\:\mathrm{note}\:\mathrm{the} \\ $$$$\mathrm{continuation}… \\ $$
Commented by mr W last updated on 17/Apr/22
other things in life come first...
$${other}\:{things}\:{in}\:{life}\:{come}\:{first}… \\ $$
Commented by Shrinava last updated on 17/Apr/22
yes of course sir
$$\mathrm{yes}\:\mathrm{of}\:\mathrm{course}\:\boldsymbol{\mathrm{sir}} \\ $$
Commented by mr W last updated on 22/Apr/22
proof see Q168926
$${proof}\:{see}\:{Q}\mathrm{168926} \\ $$
Commented by Shrinava last updated on 23/Apr/22
Yes dear sir
$$\mathrm{Yes}\:\mathrm{dear}\:\mathrm{sir} \\ $$

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