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 \(KL\).

Theme : Geometry Triangle

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## Comments

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TopNewestI will participate \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\) \(\ddot\smile\)

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Comment deleted Apr 12, 2015

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Yeah ,it's correct . Looks like you'll win this contest for sure :P

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Well , Euclid will become angry and will come for revenge on seeing my uploaded diagram above. :P :D xD

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Even I thought there was something wrong with the problem! Your proof is flawless. Just to clarify, ahead of \(E\) being the midpoint of \(AC\), you can say that \(E\) was chosen to lie on \(XC\). Hence, \(A\) and \(B\) are coincident and the triangle cannot be formed.

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Q4 has been updated.

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Q4 has been updated.

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Thanks a lot!

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Yes you are right. I am thinking of removing it. I will add another one in place of it.

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Actually this suspicion came by @Omkar Kulkarni 's median contradiction.

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

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

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

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Why the hell is the Contest Cancelled? o.O

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Rajdeep would you suggest some books for RMO

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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?

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Yes. You can send the photos.

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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.

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Yes, Of course.

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Okay :)

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I will participate

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Deadline is Near

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All the best !

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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 :)

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Deadline is near

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OPC2

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@Rajdeep Dhingra

Where is

Gin the figure to the first question ?Log in to reply

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

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

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dotthat's come out of nowhere ;)Log in to reply

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@Sandeep Bhardwaj @Azhaghu Roopesh M @megh choksi @Daniel Liu @Prasun Biswas @Parth Bhardwaj @Cody Martin

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

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

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You noticed it too ! That Megh was online today .

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Yes

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@Azhaghu Roopesh M Let's see. :) :) :)

I am also participating.Log in to reply

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