Problems of the day (Day 1)

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Moon
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Problems of the day (Day 1)

Unread post by Moon » Wed Feb 16, 2011 12:32 pm

Problem 1:
Consider a circle with diameter $AB$ and center $O$, and let $C$ and $D$ be two points on this circle. The line $CD$ meets the line $AB$ at a point $M$ satisfying $MB < MA$ and $MD < MC$. Let $K$ be the point of intersection (different from $O$) of the circumcircles of triangles $AOC$ and $DOB$. Show that $\angle MKO = 90^{\circ}$

Problem 2:
Find, with proof, all real number solutions to the following:\[
(a^2 + 1)(b^2 + 1) = (ab + 1)(a + b)\]


Source:
1. Zhao_W_C_09_cyclic quad 2
2. Buffet 2
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FahimFerdous
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Re: Problems of the day (Day 1)

Unread post by FahimFerdous » Wed Feb 16, 2011 10:44 pm

Moon vaia, as I'm using mobile, I can't see the signs properly. Please tell me what's the relation between MB and MA, MD and MC. Write them in such a way so that I can see it in mobile.
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Moon
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Re: Problems of the day (Day 1)

Unread post by Moon » Thu Feb 17, 2011 7:44 am

oi miya....tumi opera mini use koro na kan? Opera mini diya to shob thikmoto dekha jay...

BTW
P 1: Consider a circle with diameter AB and center O , and let C and D be two points on this circle. The line CD meets the line AB at a point M satisfying MB<MA and MD<MC . Let K be the point of intersection (different from O ) of the circumcircles of triangles AOC and DOB . Show that \angle MKO=90 degree.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

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FahimFerdous
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Re: Problems of the day (Day 1)

Unread post by FahimFerdous » Thu Feb 17, 2011 2:15 pm

Vaia, ami to Opera Mini e use kori. Tobe Opera Mini 4 use kori, Opera Mini 5 na. Apni ki 5 er kotha boltesen?
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Cryptic.shohag
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Re: Problems of the day (Day 1)

Unread post by Cryptic.shohag » Thu Feb 17, 2011 2:41 pm

Opera 4 diyei dkha jay. Tomar ki image off kora naki?
Jodi ta na hoy tahole web address lekhar jaygatay opera:config likhe click koro. Then last option ta no theke yes kore save koro. R jodi tateo na hoy tahole Allah tomar shohay houn....
God does not care about our mathematical difficulties; He integrates empirically. ~Albert Einstein

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Moon
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Re: Problems of the day (Day 1)

Unread post by Moon » Thu Feb 17, 2011 3:34 pm

Amio opera mini 4 use kori...
viewtopic.php?p=599&f=9#p599
Ei post er last e dekho...opera mini configuration gula dewa ase...I hope this helps.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

Hasib
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Re: Problems of the day (Day 1)

Unread post by Hasib » Thu Feb 17, 2011 4:41 pm

ki bepar! Sobai forum er rule break kortase! Half bangla kicu english! Eita kicu hoilo!
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Re: Problems of the day (Day 1)

Unread post by FahimFerdous » Thu Feb 17, 2011 4:59 pm

Thanks, Moon vaia. I can see the equations now. :D
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Nadim Ul Abrar
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Re: Problems of the day (Day 1)

Unread post by Nadim Ul Abrar » Sun Jun 12, 2011 5:27 pm

Prob.2
(a,b)=(1,1)
Proof Amar Cache Ache But Likhte Eccha Korche na :-)
$\frac{1}{0}$

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Nadim Ul Abrar
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Re: Problems of the day (Day 1)

Unread post by Nadim Ul Abrar » Sun Jun 12, 2011 5:28 pm

Moon Bhaia , Ans Ta Hoise Na.????
$\frac{1}{0}$

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