## Triangle geometry

For students of class 9-10 (age 14-16)
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Joined: Sun Dec 10, 2017 3:59 pm

### Triangle geometry

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

Tasnood
Posts: 73
Joined: Tue Jan 06, 2015 1:46 pm

### Re: Triangle geometry

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]

Mathlomaniac
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Joined: Wed Mar 07, 2018 11:35 pm
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### Re: Triangle geometry

Using ceva's theorem answer came 0.

soyeb pervez jim
Posts: 21
Joined: Sat Jan 28, 2017 11:06 pm

### Re: Triangle geometry

i think it was 2017 BdMO regional qustion

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: Triangle geometry

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.

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: Triangle geometry

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