Search found 217 matches
- Thu Mar 08, 2012 1:14 am
- Forum: Geometry
- Topic: An interesting Problem from Romanian TST
- Replies: 4
- Views: 2838
Re: An interesting Problem from Romanian TST
opposite angles of this quad are equal.
- Wed Mar 07, 2012 11:52 pm
- Forum: Geometry
- Topic: NICE GEOMETRY PROBLEM
- Replies: 3
- Views: 2516
NICE GEOMETRY PROBLEM
This the nicest problem I have ever made. Let $D$ be a point on side $AC$ of $\triangle ABC$.$E$ is the reflection of $A$ across $BD$. Pick a point $M$ on line $DE$. The line perpendicular to $BD$ at $D$ intersects $AM$ at $F$. $DF$ and $CM$ intersect at $Y$. $BD$ and $AM$ intersect at $X$. Prove th...
- Wed Mar 07, 2012 4:12 pm
- Forum: Algebra
- Topic: SL 1982 B1
- Replies: 5
- Views: 3164
Re: SL 1982 B1
i have many problms with latex.2p[-1] is divisible by p[1]+p[-1]-2[1+p[0]].
- Wed Mar 07, 2012 4:08 pm
- Forum: Algebra
- Topic: SL 1982 B1
- Replies: 5
- Views: 3164
SL 1982 B1
this a very easy problem using only school algebra.$P(x)$ is a cubic monic polynomial with integer coefficients.one of its roots is equal to the product of the other two.show that \[2P ( -1 )\]
is divisible by\[P ( 1 )+P ( -1 )-2 ( 1+P ( 0 ) )\]
is divisible by\[P ( 1 )+P ( -1 )-2 ( 1+P ( 0 ) )\]
- Wed Mar 07, 2012 3:35 pm
- Forum: Geometry
- Topic: IMO shortlist 2010 G5
- Replies: 6
- Views: 3515
Re: IMO shortlist 2010 G5
thank u saurav da.your hint works.i at last come up with a solution.made many stupid costractions and angle chasing.but what did u do with half turn where i only found a cyclic quad.but that didnt help.and mahi i didnt mean he was none of the solvers. i only wanted to mean it was a hard problem.
- Tue Mar 06, 2012 5:46 pm
- Forum: Geometry
- Topic: IMO 5 1991
- Replies: 4
- Views: 2768
Re: IMO 5 1991
the compendium solution came to my head first
- Tue Mar 06, 2012 5:39 pm
- Forum: Number Theory
- Topic: An interesting LL problem of IMO 1971
- Replies: 4
- Views: 2847
Re: An interesting LL problem of IMO 1971
not square of the sum.sum of the square
- Tue Mar 06, 2012 5:35 pm
- Forum: Geometry
- Topic: IMO shortlist 2010 G5
- Replies: 6
- Views: 3515
Re: IMO shortlist 2010 G5
did u solve it.last year in main camp we faced this prblm in an exam.none could solve it.
- Mon Mar 05, 2012 7:04 pm
- Forum: Algebra
- Topic: Beginning polynomial (Very easy)
- Replies: 2
- Views: 1971
Re: Beginning polynomial (Very easy)
sorry for 0y huge gap.
- Mon Mar 05, 2012 7:03 pm
- Forum: Algebra
- Topic: Beginning polynomial (Very easy)
- Replies: 2
- Views: 1971
Re: Beginning polynomial (Very easy)
let,d\[\leq \]
p-2.then build a contradiction.for this we can use lagrange interpolation formula.or induction to prove the lemma of compendium.that lemma can also be proved by difference operator.
p-2.then build a contradiction.for this we can use lagrange interpolation formula.or induction to prove the lemma of compendium.that lemma can also be proved by difference operator.