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Algebra

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Joined:	10 Nov 2009
Post:	13

31 Jan 2011 12:51:23 IST

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1838

inmo 2011

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

i am from 10 std. i got 35 marks in rmo and was selected for inmo on 6th feb 2011.how should i prepare?

Comments (5)

rishabh

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Joined: 25 Sep 2010

Posts: 85

31 Jan 2011 13:34:04 IST

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nice man.

Vichar Shroff

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Joined: 10 Nov 2009

Posts: 13

31 Jan 2011 14:44:51 IST

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good question

can be done by extending the side AC (b) to D such that ad=ab and by similarity in triangles ABC and BDC,we get AC/BC=BC/DC.thus a/b=b+c/a and a^2=b(b+c)

I have seen it somewhere before.Maybe an old rmo question?

Hari Shankar

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Joined: 28 Feb 2007

Posts: 2185

31 Jan 2011 15:13:43 IST

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Congratulations Vichar!

Well as you have very little time left, I would suggest visiting mathlinks.ro

This is an international forum is most used by students preparing for math olympiads across the world

There is a large bank of questions from contests across the world over several years which you will find very useful

@rishabh.

The angles A,B,C of the triangle are

Hence

So the questions wants us to prove that

But this is true as

rahulmishra

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Joined: 16 Jan 2010

Posts: 318

31 Jan 2011 19:08:19 IST

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one question for your preparation,In a triangle ABC, angle A is twice angle B. Show thata^2 = b · (b + c).

Can i try it? -> thanks

The question can be represented in the figure above....!!

We join vertex A with a point D on BC such that AD becomes the angle bisector of BAC

Now, by angle bisector theorem

c/b = m/n

=> c/b + 1 = m/n + 1

=> (b + c)/b = (m + n)/n

=> (b + c)/b = a/n ------- (i)

One more thing can be noted is

triangle ABD is isocelous

=> AD = BD = m

Again, LADC = x + x = 2x

or, LADC = 2x

So we see triangle ABC and DAC are similar (By AAA - criterion)

=> AB/AD = BC/AC = AC/CD

=> c/m = a/b = b/n

or, a/b = b/n

=> n = b²/a

putting, the value of n in (i) we get,

(b + c)/b = a/b²/a

=> a² = b.(b + c) proved..!!

Well if it was a question from RMO (then this is the first time that i could solve one on my own ha ha...!!)

rahulmishra

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Joined: 16 Jan 2010

Posts: 318

31 Jan 2011 19:17:15 IST

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@Prophet sir-> Dear sir, i am a great fan of yours, please tell me how can i be excellent at Maths... Generally i do little errors in my maths examination, how to concentrate, focus and solve it wonderfully as you do?

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