REGIONAL OLYMPIAD PROBLEM
BANGLADESH GONIT OLYMPIAD(JUNIOR) ER CTG 2013 ER 9 NO PARTISINA . KEO KI HELP KORBEN?
- asif e elahi
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- Location:Sylhet,Bangladesh
Re: REGIONAL OLYMPIAD PROBLEM
Post the problem.Ishmam! wrote:BANGLADESH GONIT OLYMPIAD(JUNIOR) ER CTG 2013 ER 9 NO PARTISINA . KEO KI HELP KORBEN?
Re: REGIONAL OLYMPIAD PROBLEM
And, use Bangla Fonts to type Bnagla. You can install Avro...it's very easy...
- Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Re: REGIONAL OLYMPIAD PROBLEM
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
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
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
Re: REGIONAL OLYMPIAD PROBLEM
Opened a separate thread for the problem:
Chittagong Junior 2013 / 9
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
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