BDMO NATIONAL JUNIOR 2015/02

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Math Mad Muggle
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BDMO NATIONAL JUNIOR 2015/02

Unread post by Math Mad Muggle » Fri Jan 27, 2017 9:18 am

Please explain the solution
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ahmedittihad
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Re: BDMO NATIONAL JUNIOR 2015/02

Unread post by ahmedittihad » Fri Jan 27, 2017 1:08 pm

You should look up the method of slicing and dicing. These type of geometry problems require the figures to be cut and thenn have their area found.

As the smaller circle is $1/2$ in diameter wrt the bigger circle, it's area is $1/4$ of the bigger one. Also, each region cut by the two lines are $1/4$ of the bigger circle. Use this.
Frankly, my dear, I don't give a damn.

Absur Khan Siam
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Re: BDMO NATIONAL JUNIOR 2015/02

Unread post by Absur Khan Siam » Sun Jan 29, 2017 10:25 pm

The answer will be $\frac{25}{2}$
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid

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samiul_samin
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Re: BDMO NATIONAL JUNIOR 2015/02

Unread post by samiul_samin » Sat Feb 23, 2019 2:23 pm

Solution:
$[x]$ denote the area of $x$
From the diagram radius of small circle=half of the radius of big circle
So,[Small Circle]=$\dfrac 14$ ×[bigcircle]=$25$

[BDC half circle]=$\dfrac 12×$[ABCD circle]=$50$

[Shaded area]=$25-12.5=12.5$

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