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

Unread post by Labib » Thu Dec 30, 2010 11:29 pm

This is a prob from Dhk div olympiad 2010....
untitled1.jpg
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.
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tushar7
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Re: Find the area??!!

Unread post by tushar7 » Fri Dec 31, 2010 2:04 am

use the ceva's theorem ..

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Tahmid Hasan
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Re: Find the area??!!

Unread post by Tahmid Hasan » Fri Dec 31, 2010 7:00 pm

it may b a silly question but r the cevian's perpendicular the the sides? :mrgreen:
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Labib
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Re: Find the area??!!

Unread post by Labib » Sat Jan 01, 2011 12:01 am

@ tahmid, no vaia!
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Labib
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Re: Find the area??!!

Unread post by Labib » Sat Jan 01, 2011 12:09 am

try Geo revisited for clarification!
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Tahmid Hasan
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Re: Find the area??!!

Unread post by Tahmid Hasan » Sat Jan 01, 2011 5:30 pm

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
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Re: Find the area??!!

Unread post by Labib » Sat Jan 01, 2011 10:49 pm

@tahmid I'm waker than you in geo. so I dont find it easy to new probs lyk this!!
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Moon
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Re: Find the area??!!

Unread post by Moon » Sun Jan 02, 2011 3:10 am

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
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Re: Find the area??!!

Unread post by Tahmid Hasan » Sun Jan 02, 2011 12:42 pm

@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
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Re: Find the area??!!

Unread post by prodip » Mon Jan 03, 2011 12:09 am

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

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