BdMO Junior 2009/9

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Hasib
Posts:238
Joined:Fri Dec 10, 2010 11:29 am
Location:খুলনা, বাংলাদেশ
Contact:
BdMO Junior 2009/9

Unread post by Hasib » Sat Feb 05, 2011 10:03 pm

One angle of a triangle is twise of another angle of the same triangle. An angle of this triangle is 120 degree. The bisector of the second largest triangle intersects its opposite side at point $D$. The distance of $D$ from the vertex containing the largest angle is $10\, cm$. If the length of the largest side of this triangle is $2x$, then a relation like the following is true:
\[x^4-C_3x^3-C_2x^2-C_1x+1875=0\]
Find the value of $C_1,C_2 \, and C_3$ analytically.
A man is not finished when he's defeated, he's finished when he quits.

Mehfuj Zahir
Posts:78
Joined:Thu Jan 20, 2011 10:46 am

Re: BdMO Junior 2009/9

Unread post by Mehfuj Zahir » Sat Feb 05, 2011 10:24 pm

If need solution please post the diagram.

Hasib
Posts:238
Joined:Fri Dec 10, 2010 11:29 am
Location:খুলনা, বাংলাদেশ
Contact:

Re: BdMO Junior 2009/9

Unread post by Hasib » Sat Feb 05, 2011 10:36 pm

there was no diagram in question
A man is not finished when he's defeated, he's finished when he quits.

Mehfuj Zahir
Posts:78
Joined:Thu Jan 20, 2011 10:46 am

Re: BdMO Junior 2009/9

Unread post by Mehfuj Zahir » Sat Feb 05, 2011 11:02 pm

Please create a diagram according to the question then i give u the solution

Hasib
Posts:238
Joined:Fri Dec 10, 2010 11:29 am
Location:খুলনা, বাংলাদেশ
Contact:

Re: BdMO Junior 2009/9

Unread post by Hasib » Sun Feb 06, 2011 12:42 am

i am extremely sorry. I use mobile. Thus i cant make a pix :'( :cry:
A man is not finished when he's defeated, he's finished when he quits.

User avatar
FahimFerdous
Posts:176
Joined:Thu Dec 09, 2010 12:50 am
Location:Mymensingh, Bangladesh

Re: BdMO Junior 2009/9

Unread post by FahimFerdous » Sun Feb 06, 2011 1:36 pm

Use 'cosine rule' and similarity of triangles.
Your hot head might dominate your good heart!

Hasib
Posts:238
Joined:Fri Dec 10, 2010 11:29 am
Location:খুলনা, বাংলাদেশ
Contact:

Re: BdMO Junior 2009/9

Unread post by Hasib » Sun Feb 06, 2011 6:40 pm

FahimFerdous wrote:Use 'cosine rule' and similarity of triangles.
i try this problem for two years! Still cant solute it! I will try...... Now
A man is not finished when he's defeated, he's finished when he quits.

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

Re: BdMO Junior 2009/9

Unread post by samiul_samin » Sun Feb 24, 2019 9:53 am

Hasib wrote:
Sat Feb 05, 2011 10:03 pm
One angle of a triangle is twise of another angle of the same triangle. An angle of this triangle is 120 degree. The bisector of the second largest triangle intersects its opposite side at point $D$. The distance of $D$ from the vertex containing the largest angle is $10\, cm$. If the length of the largest side of this triangle is $2x$, then a relation like the following is true:
\[x^4-C_3x^3-C_2x^2-C_1x+1875=0\]
Find the value of $C_1,C_2 \, and C_3$ analytically.
Solved here.

Post Reply