Search found 66 matches

by shehab ahmed
Sat May 26, 2012 8:12 pm
Forum: Biology
Topic: pressure?
Replies: 6
Views: 4566

Re: pressure?

মাথায় অক্সিজেনের অভাব হলে হাই আসে
by shehab ahmed
Sat May 26, 2012 2:14 pm
Forum: National Math Camp
Topic: Circumcentre এর লীলাখেলা
Replies: 1
Views: 1399

Re: Circumcentre এর লীলাখেলা

Hint
if one vertex of a triangle is $0$ and the other two vertices are $x$ and $y$ then the circumcentre of that triangle is given by
$\frac {xy(x'-y')}{x'y-xy'}$ where $a'$ is the conjugate of $a$
by shehab ahmed
Fri May 25, 2012 7:34 pm
Forum: National Math Camp
Topic: Circumcentre এর লীলাখেলা
Replies: 1
Views: 1399

Circumcentre এর লীলাখেলা

Let ABCD be a quadrilateral.AC and BD intersect at P.Let the circumcentres of ADP and BPC are Q and R respectively.Let the midpoints of AC,BD and QR are M,N,O respectively.Prove that the circumcentre of MNP is O
by shehab ahmed
Fri May 25, 2012 7:23 pm
Forum: International Mathematical Olympiad (IMO)
Topic: ISL 2006
Replies: 3
Views: 1867

ISL 2006

Let ABCDE be a convex pentagon such that
$\angle BAC= \angle CAD= \angle DAE$ and
$ \angle ABC= \angle ACD= \angle ADE$
If $BD$ and $CE$ intersect at $P$,then prove that $AP$ bisects $CD$.
by shehab ahmed
Fri May 25, 2012 5:17 am
Forum: Number Theory
Topic: AIME-2001
Replies: 1
Views: 1015

Re: AIME-2001

note that $1001=7*11*13$
as $j>i$ we have $10^{j-i}$ is congruent to $1 \pmod 7,11,13$
find the order of $10 \pmod {7,11,13}$ these numbers and use the following lemma
if b is the order of $a \pmod c$ and $d$ is any positive integer such that $a^d \equiv 1 \pmod c$ then, $b \mid d$
by shehab ahmed
Sat May 19, 2012 12:33 pm
Forum: International Mathematical Olympiad (IMO)
Topic: ISL 1996
Replies: 1
Views: 1214

ISL 1996

Let,H be the orthocentre of the triangle ABC and P an arbitrary point of its circumcircle.Let E the foot of the perpendicular BH and let PAQB and PARC be parallelograms.If AQ and HR intersect at X then prove that EX is parellel to AP
by shehab ahmed
Fri May 18, 2012 11:03 pm
Forum: Algebra
Topic: IMO-1992-2
Replies: 9
Views: 2366

Re: IMO-1992-2

ও আচ্ছা।ধন্যবাদ মাহি।এটা আমার মনে ছিল না।
additional property of f:
$f(x)^2=f(x^2)$ now if $x$ is non negative, then putting $x=x^{\frac {1}{2}}$ we have $f(x)$ is non negative.So we can use cauchy.
by shehab ahmed
Fri May 18, 2012 10:57 pm
Forum: Algebra
Topic: IMO-1992-2
Replies: 9
Views: 2366

Re: IMO-1992-2

হায়রে,মোবাইল থেকে কিচ্ছু বুঝতে পারছি না।আন্দাজের উপর ডোমেন এবং কো ডোমেন ধরে নিয়ে অঙ্ক করা শুরু করেছি।একটু সোজা বাংলায় ডোমেন এবং কোডোমেন কী তা বলে দিলে ভাল হত
by shehab ahmed
Fri May 18, 2012 8:26 pm
Forum: Algebra
Topic: IMO-1992-2
Replies: 9
Views: 2366

Re: IMO-1992-2

After 4th step,
5.put $y=0$ to get $f(x^2)=f(x)^2$
6.Now put $y=f(x)$ and use the equation in the 5th step to get a Cauchy's equation.
Hence,$f(x)=cx$ for some constant $c$.Checking ensures that $c=1$
by shehab ahmed
Fri May 18, 2012 8:19 pm
Forum: Algebra
Topic: IMO-1992-2
Replies: 9
Views: 2366

Re: IMO-1992-2

দুঃখিত,আমার চতুর্থ স্টেপের পর ভুল আছে।