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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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