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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
3 years, 10 months ago

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I don't think this is from IMO (International Mathematical Olympiad). Zi Song Yeoh · 3 years, 10 months ago

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@Zi Song Yeoh This is from an exam conducted here in India by a private company. Vikram Waradpande · 3 years, 10 months ago

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@Vikram Waradpande Oh, I see. Indian Mathematical Olympiad? Zi Song Yeoh · 3 years, 10 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 · 3 years, 10 months ago

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@Pranav Arora its called international mathematics olympiad conducted by SOF Jun Das · 3 years, 9 months ago

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@Zi Song Yeoh Nope. Its a basic level contest conducted by a company. Vikram Waradpande · 3 years, 10 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 · 3 years, 10 months ago

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@Kishan K YOU,RE RIGHT!. It is a problem from the work book. Neha Adepu · 3 years, 10 months ago

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

Let \(\angle A= \theta\). So, \(cos \theta = \frac{AE}{AD} =\frac{1}{2}\)

\(\implies \theta =60^o\) \(\implies \angle A=60^o\) and \(\angle B=180^o-60^o=120^o\)(As they are interior opposite angles) Maharnab Mitra · 3 years, 10 months ago

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ANGLE A=60 ANGLE B=120 Avishkar Rajeshirke · 3 years, 10 months ago

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Consider- \(DA = x\)

\(AE = x/2\)

\(EB = x/2\)

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

\(DB = x\) (Pythagoras Theorem)

\(DA = x , DB = x , AB = x\)

\(ADB\) is an Equilateral triangle

Thus, \(A = 60°\) \(B = 120°\) Rashmi B K · 3 years, 10 months ago

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@Rashmi B K THANK YOU!!! Neha Adepu · 3 years, 10 months ago

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I think is 180 degrees Yen Loong · 3 years, 10 months ago

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This que is not from IMO ! Rashmi B K · 3 years, 10 months ago

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If this problem is from IMO, please tell me what year and what question. Anton Than Trong · 3 years, 10 months ago

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@Anton Than Trong Thats Indian Maths Olympiad Avishkar Rajeshirke · 3 years, 10 months ago

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@Anton Than Trong this problem is not from the main exam, it is from the workbook Neha Adepu · 3 years, 10 months ago

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