Problem from IMO

ABCD is a rhombus in which the altitude from d bisects AB. AE=EB. Therefore, angle A and angle B respectively are (of how many degrees).

Note by Neha Adepu
5 years, 12 months ago

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3 votes

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I don't think this is from IMO (International Mathematical Olympiad).

Zi Song Yeoh - 5 years, 12 months ago

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This is from an exam conducted here in India by a private company.

Vikram Waradpande - 5 years, 12 months ago

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Oh, I see. Indian Mathematical Olympiad?

Zi Song Yeoh - 5 years, 12 months ago

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@Zi Song Yeoh No way, I doubt they ask such easy questions. As Vikram said, it must be a contest by some private organisation.

If the private organisations use names such as "IMO" and mislead the students, then its a very bad tactic to promote themselves.

Pranav Arora - 5 years, 12 months ago

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@Pranav Arora its called international mathematics olympiad conducted by SOF

Jun Das - 5 years, 11 months ago

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@Zi Song Yeoh Nope. Its a basic level contest conducted by a company.

Vikram Waradpande - 5 years, 12 months ago

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Hey guys,I think she is talking of SOF IMO and not the Great and the one you all are thinking IMO!!!!

Kishan k - 5 years, 12 months ago

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YOU,RE RIGHT!. It is a problem from the work book.

neha adepu - 5 years, 12 months ago

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Consider the sides of the rhombus to be of length xx, i.e., AD=xAD=x. So, AE=x2AE= \frac{x}{2}.

Let A=θ\angle A= \theta. So, cosθ=AEAD=12cos \theta = \frac{AE}{AD} =\frac{1}{2}

    θ=60o\implies \theta =60^o     A=60o\implies \angle A=60^o and B=180o60o=120o\angle B=180^o-60^o=120^o(As they are interior opposite angles)

Maharnab Mitra - 5 years, 12 months ago

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This que is not from IMO !

Rashmi B K - 5 years, 12 months ago

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I think is 180 degrees

Yen Loong - 5 years, 12 months ago

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Consider- DA=xDA = x

AE=x/2AE = x/2

EB=x/2EB = x/2

DE=x2(x/2)2DE = x^{2} - (x/2)^{2} =3x/2= \sqrt{3}x/2

DB=xDB = x (Pythagoras Theorem)

DA=x,DB=x,AB=xDA = x , DB = x , AB = x

ADBADB is an Equilateral triangle

Thus, A=60°A = 60° B=120°B = 120°

Rashmi B K - 5 years, 12 months ago

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THANK YOU!!!

neha adepu - 5 years, 12 months ago

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ANGLE A=60 ANGLE B=120

Avishkar Rajeshirke - 5 years, 12 months ago

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If this problem is from IMO, please tell me what year and what question.

Anton Than Trong - 5 years, 12 months ago

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Thats Indian Maths Olympiad

Avishkar Rajeshirke - 5 years, 12 months ago

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this problem is not from the main exam, it is from the workbook

neha adepu - 5 years, 12 months ago

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