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|dw:1345656175855:dw|

yes sir..

r=1 here..from cosine law ..

thats right...

but didn't u mention AB as sqrt( 2 + sqrt(2) )

ohh yes,,its sqrt( 2 + sqrt(2) ) and not 2 + sqrt(2) @mukushla

sorry...yes

|dw:1345656382986:dw|

ohh wait,,i reach some where..

thats right...

aha..so how do we continue ? AM,GM ? i dont think will help much ?

i think there are better methods...this one seems a little bit hard to get

hmm..

gradient ?

http://en.wikipedia.org/wiki/Gradient

so gradient approximately means slope ?

i mean in layman language ?

It replaces derivative in functions of two variables,

yep,,that only,,
so how do you make that conclusion from derivatives ?

Have you had calculus III?

nops..am just high school pass sir,, :/

Ok. May be there is a more elementary method. Let us hope someone else will find it.

hmm..

is AB parallel to CD?

is this correct?\[\frac{\sin a+\sin b+\sin c}{3} \le \sin \frac{a+b+c}{3}\]

I was just looking for possible entries. I didn't want to rely on the drawing above.

to my understanding u can use Jensen's inequality here...

see if this might help
http://www.artofproblemsolving.com/Wiki/index.php/Cyclic_quadrilateral

http://www.onlinemathlearning.com/quadrilateral-circle.html

muku, I like how you manipulated this one.

I think the key is in cyclic quadrilateral