## BDMO Divisional_2014

Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Tasnood
Posts: 11
Joined: Tue Jan 06, 2015 1:46 pm

### BDMO Divisional_2014

The area of ABC and OBC triangle is 120 and 24 respectively. BC=16, EF=8. Find out the area of OEAF Quadrilateral.
Attachments
Capture.JPG (13.2 KiB) Viewed 301 times

dshasan
Posts: 66
Joined: Fri Aug 14, 2015 6:32 pm

### Re: BDMO Divisional_2014

\$EF = \dfrac{1}{2} BC\$ so,\$EF \parallel BC\$

So, \$\bigtriangleup AEF = \dfrac{1}{4}\bigtriangleup ABC = 30\$

Now, \$\bigtriangleup OEF\$ is similar to \$\bigtriangleup OBC\$

So, \$\dfrac{\bigtriangleup OEF}{\bigtriangleup OBC} = \dfrac{EF^2}{BC^2} = \dfrac{1}{4}\$

\$\Rightarrow \bigtriangleup OEF = 6\$

SO, area of \$OEAF = \bigtriangleup AEF + \bigtriangleup OEF = 30 + 6 = 36\$
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

- Charles Caleb Colton

Tasnood
Posts: 11
Joined: Tue Jan 06, 2015 1:46 pm

### Re: BDMO Divisional_2014

You can't say EF||BC only to see that EF=BC/2. Because E and F mayn't be the midpoints. Thanks