REGIONAL OLYMPIAD PROBLEM

For students of class 6-8 (age 12 to 14)
User avatar
Ishmam!
Posts:2
Joined:Wed Jan 15, 2014 12:09 pm
REGIONAL OLYMPIAD PROBLEM

Unread post by Ishmam! » Wed Jan 15, 2014 12:17 pm

BANGLADESH GONIT OLYMPIAD(JUNIOR) ER CTG 2013 ER 9 NO PARTISINA . KEO KI HELP KORBEN?

User avatar
asif e elahi
Posts:185
Joined:Mon Aug 05, 2013 12:36 pm
Location:Sylhet,Bangladesh

Re: REGIONAL OLYMPIAD PROBLEM

Unread post by asif e elahi » Wed Jan 15, 2014 7:42 pm

Ishmam! wrote:BANGLADESH GONIT OLYMPIAD(JUNIOR) ER CTG 2013 ER 9 NO PARTISINA . KEO KI HELP KORBEN?
Post the problem.

User avatar
sowmitra
Posts:155
Joined:Tue Mar 20, 2012 12:55 am
Location:Mirpur, Dhaka, Bangladesh

Re: REGIONAL OLYMPIAD PROBLEM

Unread post by sowmitra » Thu Jan 16, 2014 4:07 pm

And, use Bangla Fonts to type Bnagla. You can install Avro...it's very easy... :)
"Rhythm is mathematics of the sub-conscious."
Some-Angle Related Problems;

User avatar
Thanic Nur Samin
Posts:176
Joined:Sun Dec 01, 2013 11:02 am

Re: REGIONAL OLYMPIAD PROBLEM

Unread post by Thanic Nur Samin » Fri Jan 17, 2014 9:15 pm

O,F যোগ করি। OF=ব্যাসার্ধ=OA=10।
এখন,
$OE^2+OG^2=OF^2=10^2=100.......(1)$
$2(OE+OG)=24$বা$OE+OG=12$বা$OE=12-OG..............(2)$
(1)নং এ বসিয়ে পাই,
$(12-OG)^2+OG^2=100=> 2OG^2-24OG+144=100=> OG^2-12OG+22=0=> OG=6-\sqrt{14}$
অর্থাৎ,
$OE=6+\sqrt{14}$
$OG=12-OE=6-\sqrt{14}$
কিন্তু বৃত্তকলা $(AOB)=\frac{\pi 10^2}{4}=25\pi$
সুতরাং,
$(OGE)=\frac{1}{2}\times(6+\sqrt{14})(6-\sqrt{14})=11=> (AEGBF)=(AOB)-(GOE)=-11+25\pi$
তাই উত্তর হবে $-275$
কাজের সময় পারি নাই :cry: :cry:
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

User avatar
Labib
Posts:411
Joined:Thu Dec 09, 2010 10:58 pm
Location:Dhaka, Bangladesh.

Re: REGIONAL OLYMPIAD PROBLEM

Unread post by Labib » Sun Jan 19, 2014 11:38 am

Opened a separate thread for the problem:
Chittagong Junior 2013 / 9
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Post Reply