## Search found 217 matches

Mon Feb 18, 2013 3:52 pm
Forum: Algebra
Topic: VNMO 2013
Replies: 3
Views: 1677

### Re: VNMO 2013

Define the function $f(x)=\frac{x+2}{2^x}$
$f'(x)=2^{-x}$ $(1-(x+2) ln2)$.
As $x>1$,$f'(x)<2^{-x}(1-ln8)<0$
so this function is decreasing.
Which implies the sequence $a_n$ is increasing.
Now by induction we can show that $a_n \leq 2$ for all $n$.
actually this is the limit.
Mon Feb 11, 2013 10:11 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 8
Replies: 6
Views: 3566

$A$,$X$,$C$,$Y$ cyclic.And $Z$,$X$,$S$,$Y$ cyclic.So $EZ.ES$=$EX.EY$=$EA.EC$ Let $H$ be the orthocentre.$EA.EC=EH.EB$ But $ES.EZ=EH.EB$ so $H$ is the orthocentre of $\triangle ZBS$ So $ZH$ is perpendicular to $BS$. Let $M$ be the midpoint of $AC$. $ZH$ is the polar of $B$ with respect to circle $AFD... Sat Feb 02, 2013 12:07 am Forum: Algebra Topic: Fuctional inequality Replies: 1 Views: 1193 ### Re: Fuctional inequality Telescoping yields an elegant solution. Fri Feb 01, 2013 10:52 pm Forum: National Math Olympiad (BdMO) Topic: BdMO National 2012: Secondary 8 Replies: 10 Views: 4948 ### Re: BdMO National 2012: Secondary 8 That's what stops the good ninja(me).Mis-comprehension of problem statement. Now i know how the hell u deduce those things. Fri Feb 01, 2013 10:23 pm Forum: National Math Olympiad (BdMO) Topic: BdMO National 2012: Secondary 8 Replies: 10 Views: 4948 ### Re: BdMO National 2012: Secondary 8 I don't know how the hell you deduced$EA=EE"$Because that implies$\angle E'AE"=90 ^\circ$which is not true. Fri Feb 01, 2013 10:04 pm Forum: National Math Olympiad (BdMO) Topic: BdMO National 2012: Secondary 8 Replies: 10 Views: 4948 ### Re: BdMO National 2012: Secondary 8 I don't know how the hell you deduced that$\angle ECA=2\angle EAC$.Please explain. Your solution is incorrect. Thu Jan 31, 2013 7:11 pm Forum: National Math Olympiad (BdMO) Topic: BdMO Higher secondary solutions Replies: 13 Views: 10572 ### Re: BdMO Higher secondary solutions TIUrmi wrote:ইতিহাসে আমার নাম স্বর্ণাক্ষরে লেখা থাকবে সেই আনন্দে আমার কান্না পাচ্ছে। এই কথা পড়ে আমার হাসি পাচ্ছে। Wed Jan 30, 2013 2:30 pm Forum: Divisional Math Olympiad Topic: Rajshahi MO 2013, Secondary 1 Replies: 9 Views: 3804 ### Re: Rajshahi MO 2013, Secondary 1 Oi Mahi,that makes use of such a big assumption as for those$4$points ,the diagonals intersect strictly inside the hull.But we can get$3$intersection points.Namely for points$A$,$B$,$C$,$D$,$AB \cap CD$,$AD \cap BC$and$AC \cap BD\$.
Sat Jan 26, 2013 12:16 am
Forum: Primary Level
Topic: palindrome number
Replies: 5
Views: 6442

### Re: palindrome number

Prosenjit,
Your solution is close to brute force.you have to show that 11 must divide them.Eventually in order to be a perfect square 121 must divide them.Which is not possible.
Fri Jan 25, 2013 11:31 pm
Forum: Geometry
Topic: Geometry Marathon v1.0
Replies: 23
Views: 10955

### Re: Geometry Marathon v1.0

I like this marathon.I am so glad that i am posting in the same marathon as our predecessors.
Why don't we run this marathon?