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Trignometry
17 Feb 2007 21:42:06 IST
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Shakir n all the gang, try out this one
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Hiiiiii folks,
here's one question in which m badly stuck....
in a triangle ABC, the medians BE and CD intersect at right angles, then find the minimum value of cotB + cot C.....
the answer is,(as u all we would hav guessed,) 2/sqrrt3....but i wanna knw the complete method of this question!!!
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avdesh100
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Joined: 9 Feb 2007
Posts: 471
17 Feb 2007 22:51:34 IST
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check out the physics solution.
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18 Feb 2007 21:55:19 IST
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(cotA+cotB+cotC)/3>=cot((A+B+C)/3)
cotB+cotC=sqroot(3)-cotA
this equality will hold only if A=B=C
then cotA+cot B=2/sqroot(3)
in equilateral triangle anglebisectors and medians r same and intersect at 90
but the problem is i havent used the prop that they intersect at right angles!!!!
that was why i was suggesting draw semicircles and use some gd prop there
cotB+cotC=sqroot(3)-cotA
this equality will hold only if A=B=C
then cotA+cot B=2/sqroot(3)
in equilateral triangle anglebisectors and medians r same and intersect at 90
but the problem is i havent used the prop that they intersect at right angles!!!!
that was why i was suggesting draw semicircles and use some gd prop there
18 Feb 2007 21:56:25 IST
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btw shakir have u solved the physics subjective question in open test whr, thr were 5 plates nd some charge were given on it nd then potential difference was asked..... wat hav u got the answer??? m getting it 2 and the answer given in solution is 1....wat was urs???
...... nd if directly we take A=B=C, we can put the value of cot 60 directly....isnt it???18 Feb 2007 21:59:54 IST
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i did nt do that in paper but yes i tried at home and im vry confused that it is comin 2 as u r sayin .
ya really a silly mistake i have commited actually bcoz i is a big doubt of urs i think i will have to solve the problem on paper. an draw diagram
18 Feb 2007 22:09:51 IST
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no shortcut yaar, the way we give charge +q nd -q, n then apply charge conservation and that electric field inside conductor=0, frm here we get the values of charge induced n then potential difference can be calculated easily...its too lengthy, infact it took quite lot of tym then!!!
By AM - GM inequality
cotBcotC..............(1)
19 Feb 2007 19:21:52 IST
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I think we can as well solve this way...
assume G be the centroid..
Let <GBC=B1 and <GBA=B2 and GB=x GC=y
now from rt triangles BDG and BGC, we can find cot<B1 and cot<B2
apply compound angle formula for cot<B1+B2
similarly for<C and adding both we get an algebraic eqn in x,y
hence we can find its minimum....
this has no restrictions for <B and <C
goutham
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