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BdMO Junior 2009/9
Posted: Sat Feb 05, 2011 10:03 pm
by Hasib
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.
Re: BdMO Junior 2009/9
Posted: Sat Feb 05, 2011 10:24 pm
by Mehfuj Zahir
If need solution please post the diagram.
Re: BdMO Junior 2009/9
Posted: Sat Feb 05, 2011 10:36 pm
by Hasib
there was no diagram in question
Re: BdMO Junior 2009/9
Posted: Sat Feb 05, 2011 11:02 pm
by Mehfuj Zahir
Please create a diagram according to the question then i give u the solution
Re: BdMO Junior 2009/9
Posted: Sun Feb 06, 2011 12:42 am
by Hasib
i am extremely sorry. I use mobile. Thus i cant make a pix :'(
Re: BdMO Junior 2009/9
Posted: Sun Feb 06, 2011 1:36 pm
by FahimFerdous
Use 'cosine rule' and similarity of triangles.
Re: BdMO Junior 2009/9
Posted: Sun Feb 06, 2011 6:40 pm
by Hasib
FahimFerdous wrote:Use 'cosine rule' and similarity of triangles.
i try this problem for two years! Still cant solute it! I will try...... Now
Re: BdMO Junior 2009/9
Posted: Sun Feb 24, 2019 9:53 am
by samiul_samin
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.