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

Posted: Thu Dec 30, 2010 11:29 pm
by Labib
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 (8.13KiB)Viewed 11696 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.

Re: Find the area??!!

Posted: Fri Dec 31, 2010 2:04 am
by tushar7
use the ceva's theorem ..

Re: Find the area??!!

Posted: Fri Dec 31, 2010 7:00 pm
by Tahmid Hasan
it may b a silly question but r the cevian's perpendicular the the sides? :mrgreen:

Re: Find the area??!!

Posted: Sat Jan 01, 2011 12:01 am
by Labib
@ tahmid, no vaia!

Re: Find the area??!!

Posted: Sat Jan 01, 2011 12:09 am
by Labib
try Geo revisited for clarification!

Re: Find the area??!!

Posted: Sat Jan 01, 2011 5:30 pm
by Tahmid Hasan
my ans is 315.
@labib bhai ,i know ceva's thm.
i used the thm and some proportions to make a quadratic equation ::mrgreen::

Re: Find the area??!!

Posted: Sat Jan 01, 2011 10:49 pm
by Labib
@tahmid I'm waker than you in geo. so I dont find it easy to new probs lyk this!!

Re: Find the area??!!

Posted: Sun Jan 02, 2011 3:10 am
by Moon
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.

Re: Find the area??!!

Posted: Sun Jan 02, 2011 12:42 pm
by Tahmid Hasan
@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??????????????

Re: Find the area??!!

Posted: Mon Jan 03, 2011 12:09 am
by prodip
Please show the way of finding the area.............