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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TopNewest@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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I will participate $\ddot\smile$ $\ddot\smile$ $\ddot\smile$ $\ddot\smile$ $\ddot\smile$ $\ddot\smile$

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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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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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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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