# 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
5 years, 7 months ago

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

- 5 years, 6 months ago

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

- 5 years, 6 months ago

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

- 5 years, 6 months ago

Why the hell is the Contest Cancelled? o.O

- 5 years, 6 months ago

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.

- 5 years, 6 months ago

Okay. No problem. :)

- 5 years, 6 months ago

Rajdeep would you suggest some books for RMO

- 5 years, 6 months ago

@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?

- 5 years, 6 months ago

Yes. You can send the photos.

- 5 years, 6 months ago

@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.

- 5 years, 6 months ago

Yes, Of course.

- 5 years, 6 months ago

Okay :)

- 5 years, 6 months ago

I will participate

- 5 years, 6 months ago

- 5 years, 6 months ago

All the best !

- 5 years, 6 months ago

I will participate $\ddot\smile$ $\ddot\smile$ $\ddot\smile$ $\ddot\smile$ $\ddot\smile$ $\ddot\smile$

- 5 years, 7 months ago

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

- 5 years, 7 months ago

- 5 years, 6 months ago

- 5 years, 7 months ago

Where is G in the figure to the first question ?

- 5 years, 7 months ago

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

- 5 years, 7 months ago

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

- 5 years, 7 months ago

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

- 5 years, 7 months ago

Yeah , fine .

- 5 years, 7 months ago

Done it.

- 5 years, 7 months ago

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

- 5 years, 7 months ago

Yes. Just a editing mistake.

- 5 years, 7 months ago

Ok .

- 5 years, 7 months ago

- 5 years, 7 months ago

You noticed it too ! That Megh was online today .

- 5 years, 7 months ago

Yes

- 5 years, 7 months ago

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

- 5 years, 7 months ago

Challenge accepted :P

- 5 years, 7 months ago

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

- 5 years, 7 months ago

No Problem. Best of luck.

- 5 years, 7 months ago

Thanks :)

- 5 years, 7 months ago

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

- 5 years, 7 months ago

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

- 5 years, 7 months ago