BDMO NATIONAL JUNIOR 2015/02

Posts: 29
Joined: Mon Jan 23, 2017 10:32 am

BDMO NATIONAL JUNIOR 2015/02

Attachments
Screenshot_2017-01-27-09-14-49-1.png (47.81 KiB) Viewed 1598 times

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.
Frankly, my dear, I don't give a damn.

Absur Khan Siam
Posts: 65
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]=$25-12.5=12.5$