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Triangle geometry

Posted: Sun Dec 10, 2017 4:17 pm
by MD ADNAN RAHMAN
In triangle ABC D,E,F are three points on BC,CA,AB respectively such that AE:EC=1:3, DC:DB=2:1, BF:FA=3:2, after attaching D,E,F with "shirshobindu" of opposite side, there creates another triangle HIG in the middle. what is the area of triangle HIG

Re: Triangle geometry

Posted: Tue Feb 13, 2018 7:47 pm
by Tasnood
Do you want to mean "Joining $AD,BE,CF$"?
Then, they intersect at a single point, no triangle comes out. [If I don't miss anything]

Re: Triangle geometry

Posted: Sun Mar 11, 2018 10:11 pm
by Mathlomaniac
Using ceva's theorem answer came 0.

Re: Triangle geometry

Posted: Wed Mar 28, 2018 8:23 pm
by soyeb pervez jim
i think it was 2017 BdMO regional qustion

Re: Triangle geometry

Posted: Fri Mar 30, 2018 11:27 am
by samiul_samin
soyeb pervez jim wrote:
Wed Mar 28, 2018 8:23 pm
i think it was 2017 BdMO regional qustion
Yes and it is discussed before in this forum.

Re: Triangle geometry

Posted: Sun Feb 17, 2019 3:20 pm
by samiul_samin
MD ADNAN RAHMAN wrote:
Sun Dec 10, 2017 4:17 pm
In triangle $ABC$. $D,E,F$ are three points on $BC,CA,AB$ respectively such that $AE:EC=1:3$, $DC:DB=2:1$,$ BF:FA=3:2$, after attaching $D,E,F$ with "shirshobindu" of opposite side, there creates another triangle $HIG$ in the middle. what is the area of triangle $HIG$?
This is BdMO Mymensingh regional 2017 secondary problem 3.

Given diagram in the question:
Screenshot_2019-02-17-15-19-37-1.png
Screenshot_2019-02-17-15-19-37-1.png (11.09 KiB) Viewed 484 times