Open Proof Contest 3

Hello Every\(\displaystyle \int_0^1{dx}\).

This is the third part of the contest started by me.Here is the \(3^{rd}\) part.The rules are the same as the previous ones. You need need to mail the PDFs to opencontestproofs@gmail.com. To make a PDF you can go to Latex PDF. Also you can send a snip of the solution after typing it in \(\LaTeX\).

Here are the questions

1.Look at the figure below :

It is given that \(AB || GF \) and \(EFGH\) is parallelogram. Prove that \(FE || DC\) .

\(2\). Look at the figure below :

\(ABCD\) is a parallelogram and \(AXY\) is a straight line through \(A\) meeting \(BC\) at \(X\) and \(DC\) at \(Y\). Prove that \(BX\times DY\) is a constant.

\(3\).Look at the figure below:

Given four points \(A,B,C,D\) in a straight line, show that a point \(O\) exists in the same straight line such that \(OA:OB = OC:OD\).Also find that point.

\(4\).Look at the figure below:

\(PQ\) is a chord of a circle. Through the mid point \(M\) of \(PQ\) chords \(AB\) and \(CD\) are drawn. \(AD\) and \(BC\) meet \(PQ\) at \(K\) and \(L\). Then prove that \(M\) is the midpoint of \(KL\).


\[\huge \textbf{Cancelled}\]

Theme : Geometry Triangle

Note by Rajdeep Dhingra
3 years, 9 months ago

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I will participate \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\)

Mehul Arora - 3 years, 9 months ago

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@Rajdeep Dhingra , When Will you give out the results? -_-

Mehul Arora - 3 years, 8 months ago

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This contest is cancelled and we all are trolled ... xD Cheers! :( :(

Nihar Mahajan - 3 years, 8 months ago

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Why the hell is the Contest Cancelled? o.O

Mehul Arora - 3 years, 8 months ago

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@Mehul Arora Sorry for that. But since Schools are going on and I am very much busy, I can't Compile the result. I will release OPC 4 on 18th May. Do participate in that one. Sorry.

Rajdeep Dhingra - 3 years, 8 months ago

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@Rajdeep Dhingra Okay. No problem. :)

Mehul Arora - 3 years, 8 months ago

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Could you post a solution for the third one? It is troubling me SOO much.

Omkar Kulkarni - 3 years, 8 months ago

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All the best dear. You're making it Great. Keep it up. @Rajdeep Dhingra

Sandeep Bhardwaj - 3 years, 9 months ago

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Thank you sir ! You always motivate people. Proud to be your student.

Rajdeep Dhingra - 3 years, 9 months ago

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You noticed it too ! That Megh was online today .

Azhaghu Roopesh M - 3 years, 9 months ago

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Yes

Rajdeep Dhingra - 3 years, 9 months ago

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@Rajdeep Dhingra Yes . Though I'll submit my entries after the 4th .

Azhaghu Roopesh M - 3 years, 9 months ago

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@Azhaghu Roopesh M No Problem. Best of luck.

Rajdeep Dhingra - 3 years, 9 months ago

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@Rajdeep Dhingra Thanks :)

Azhaghu Roopesh M - 3 years, 9 months ago

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@Rajdeep Dhingra I am also participating. @Azhaghu Roopesh M Let's see. :) :) :)

Nihar Mahajan - 3 years, 9 months ago

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@Nihar Mahajan Challenge accepted :P

Azhaghu Roopesh M - 3 years, 9 months ago

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@Rajdeep Dhingra

Where is G in the figure to the first question ?

Azhaghu Roopesh M - 3 years, 9 months ago

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G is the point on the parallelogram. GH is parallel to EF

Rajdeep Dhingra - 3 years, 9 months ago

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I understood that , but won't you make an edit in the picture ?

Azhaghu Roopesh M - 3 years, 9 months ago

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@Azhaghu Roopesh M Right now I have to go somewhere. So I will make it in about an hour.

Rajdeep Dhingra - 3 years, 9 months ago

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@Rajdeep Dhingra Yeah , fine .

Azhaghu Roopesh M - 3 years, 9 months ago

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@Azhaghu Roopesh M Done it.

Rajdeep Dhingra - 3 years, 9 months ago

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@Rajdeep Dhingra Thanks :) But it seems there's an extra dot that's come out of nowhere ;)

Azhaghu Roopesh M - 3 years, 9 months ago

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@Azhaghu Roopesh M Yes. Just a editing mistake.

Rajdeep Dhingra - 3 years, 9 months ago

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@Rajdeep Dhingra Ok .

Azhaghu Roopesh M - 3 years, 9 months ago

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Could you provide a link to the previous ones, so as to give everyone easy access to the rules? Thanks. I'll participate too :)

Omkar Kulkarni - 3 years, 9 months ago

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OPC2

Rajdeep Dhingra - 3 years, 9 months ago

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Deadline is near

Rajdeep Dhingra - 3 years, 9 months ago

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I will participate

Samruddh Kamath - 3 years, 9 months ago

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All the best !

Rajdeep Dhingra - 3 years, 9 months ago

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Deadline is Near

Rajdeep Dhingra - 3 years, 9 months ago

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@Rajdeep Dhingra , Can I Give my solution in MS Word? I am not really familiar with LaTeX Yet. Also, Can I give my solution in Parts? I have a lot of Homework To do.

Mehul Arora - 3 years, 9 months ago

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Yes, Of course.

Rajdeep Dhingra - 3 years, 9 months ago

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Okay :)

Mehul Arora - 3 years, 9 months ago

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@Rajdeep Dhingra I had error with converting Latex to pdf.So i managed to convert Latex to photo. Is it ok if I send you photos?

Nihar Mahajan - 3 years, 9 months ago

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Yes. You can send the photos.

Rajdeep Dhingra - 3 years, 9 months ago

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Rajdeep would you suggest some books for RMO

Samruddh Kamath - 3 years, 8 months ago

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