Dhaka Higher Secondary 2010/2 (Secondary 2010/9)
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Please don't post problems (by starting a topic) in the "Higher Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can 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.
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.
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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Re: Find the area??!!
use the ceva's theorem ..
- Tahmid Hasan
- Posts: 665
- Joined: Thu Dec 09, 2010 5:34 pm
- Location: Khulna,Bangladesh.
Re: Find the area??!!
it may b a silly question but r the cevian's perpendicular the the sides?
বড় ভালবাসি তোমায়,মা
Re: Find the area??!!
@ tahmid, no vaia!
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Re: Find the area??!!
try Geo revisited for clarification!
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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"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
- Location: Khulna,Bangladesh.
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::
@labib bhai ,i know ceva's thm.
i used the thm and some proportions to make a quadratic equation ::mrgreen::
বড় ভালবাসি তোমায়,মা
Re: Find the area??!!
@tahmid I'm waker than you in geo. so I dont find it easy to new probs lyk this!!
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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.
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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learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
- Tahmid Hasan
- Posts: 665
- Joined: Thu Dec 09, 2010 5:34 pm
- Location: Khulna,Bangladesh.
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??????????????
will u consider that a shortcut??????????????
বড় ভালবাসি তোমায়,মা
Re: Find the area??!!
Please show the way of finding the area.............