## Dhaka Higher Secondary 2010/2 (Secondary 2010/9)

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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Labib
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Joined: Thu Dec 09, 2010 10:58 pm
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### Dhaka Higher Secondary 2010/2 (Secondary 2010/9)

This is a prob from Dhk div olympiad 2010....
As shown in the figure, triangle ABC is divided
into six smaller triangles by lines drawn from the
vertices through a common interior point. The
areas of four of these triangles are as indicated.
Find the area of triangle ABC.
untitled1.jpg (8.13 KiB) Viewed 2338 times
As shown in the figure, triangle ABC is divided
into six smaller triangles by lines drawn from the
vertices through a common interior point. The
areas of four of these triangles are as indicated.
Find the area of triangle ABC.
Learn how to write equations, and don't forget to read

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

tushar7
Posts: 101
Joined: Tue Dec 07, 2010 3:23 pm

### Re: Find the area??!!

use the ceva's theorem ..

Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm

### Re: Find the area??!!

it may b a silly question but r the cevian's perpendicular the the sides?
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Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm
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### Re: Find the area??!!

@ tahmid, no vaia!
Learn how to write equations, and don't forget to read

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm
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### Re: Find the area??!!

try Geo revisited for clarification!
Learn how to write equations, and don't forget to read

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm

### Re: Find the area??!!

my ans is 315.
@labib bhai ,i know ceva's thm.
i used the thm and some proportions to make a quadratic equation ::mrgreen::
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Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm
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### Re: Find the area??!!

@tahmid I'm waker than you in geo. so I dont find it easy to new probs lyk this!!
Learn how to write equations, and don't forget to read

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Moon
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
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### Re: Find the area??!!

I don't know how you expect to solve it using "only" Ceva's theorem. Moreover, I'd like to encourage you not to try finding "automatic solution", because if you do this now, and take too many shortcuts, you'll find soon that hard problems can not be solved by shortcuts. You'll need your own theorem.

Here the best way is to work with areas and ratios. Use the simple idea that when two triangles have same height their areas are proportional to their bases.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

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Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm

### Re: Find the area??!!

@moon vai,i used ceva and the law u showed 2 make a quadratic eq, that's y i meant"some propoetions".
will u consider that a shortcut??????????????
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prodip
Posts: 27
Joined: Sun Dec 19, 2010 1:24 pm

### Re: Find the area??!!

Please show the way of finding the area.............