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Trignometry

Forum Expert
 Joined: 1 Dec 2006 Post: 2108
17 Feb 2007 21:42:06 IST
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33
1892
Shakir n all the gang, try out this one
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

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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Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
17 Feb 2007 22:51:34 IST
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check out the physics solution.

Hot goIITian

Joined: 24 Nov 2006
Posts: 133
17 Feb 2007 22:55:26 IST
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manasi where are u studying

Forum Expert
Joined: 1 Dec 2006
Posts: 2108
17 Feb 2007 22:56:34 IST
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nowhere, m studying on my own....y u asked???

New kid on the Block

Joined: 16 Feb 2007
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18 Feb 2007 13:59:23 IST
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gth

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18 Feb 2007 21:24:27 IST
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Joined: 27 Dec 2006
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18 Feb 2007 21:28:05 IST
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hey manasi i just tried out ur problem and i was usin the prop
in which angle in a semi circle is 90 degree we get 3 cricles

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Joined: 1 Dec 2006
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18 Feb 2007 21:41:43 IST
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how this will help in solving the question!!!

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Joined: 27 Dec 2006
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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

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Joined: 1 Dec 2006
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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???

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Joined: 1 Dec 2006
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18 Feb 2007 21:58:10 IST
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shakir, medians of an equilateral triangle dnt intersect at rite angles, do they ...... nd if directly we take A=B=C, we can put the value of cot 60 directly....isnt it???

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Joined: 27 Dec 2006
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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

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18 Feb 2007 22:02:32 IST
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it is cuming 2.....i did it in the paer too and at home also.... nd even some of my frnds are also getting 2...but the answer given is 1....newayz thanx

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Joined: 27 Dec 2006
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18 Feb 2007 22:04:57 IST
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ya in the open test i told u dat they give some wrong solutions
can u tell me the techniques u used.
i think there must be a shortcut to solve this kind of problem

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Joined: 1 Dec 2006
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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!!!

Hot goIITian

Joined: 11 Dec 2006
Posts: 172
18 Feb 2007 22:34:08 IST
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can u post dat ques. manasi i didnot write open test

Blazing goIITian

Joined: 18 Dec 2006
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19 Feb 2007 19:03:14 IST
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By AM - GM inequality
cotB+cotC>=22cotBcotC..............(1)
For LHS 2 b min. cotB=cotC also in a triangle cotAcotB+cotBcotC+cotCcotA=1
So by taking cotBcotC=1/3 in (1) we get
Min. value of cotB+cotC=2/23
Hence proved.

Blazing goIITian

Joined: 7 Feb 2007
Posts: 544
19 Feb 2007 19:16:11 IST
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What if any one of <B or <C is obtuse??
I mean, we cant apply the inequality....
But nehow, nice soln.....would u bother helpin me in maths??
goutham

Blazing goIITian

Joined: 7 Feb 2007
Posts: 544
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

Hot goIITian

Joined: 11 Dec 2006
Posts: 172
20 Feb 2007 20:04:40 IST
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plzzzz...................... send me dat ques. im requesting
Plzzzzzzz...................................

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