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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 (11.09 KiB) Viewed 1477 times