BDMO NATIONAL JUNIOR 2015/02

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BDMO NATIONAL JUNIOR 2015/02
Please explain the solution
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 ahmedittihad
 Posts: 181
 Joined: Mon Mar 28, 2016 6:21 pm
Re: BDMO NATIONAL JUNIOR 2015/02
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.
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.

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 Joined: Tue Dec 08, 2015 4:25 pm
 Location: Bashaboo , Dhaka
Re: BDMO NATIONAL JUNIOR 2015/02
The answer will be $\frac{25}{2}$
"(To Ptolemy I) There is no 'royal road' to geometry."  Euclid
 samiul_samin
 Posts: 1007
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BDMO NATIONAL JUNIOR 2015/02
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]=$2512.5=12.5$
$[x]$ 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]=$2512.5=12.5$