Prove that, among the quadrilaterals inscribed in a circle, a square's area is the maximum.
Hint: Write the area formula in sines and notice for what $sin\theta$ is maximum.
Search found 176 matches
- Fri Jan 31, 2014 8:35 pm
- Forum: Secondary Level
- Topic: Cyclic quadrilateral
- Replies: 4
- Views: 4125
- Fri Jan 31, 2014 1:09 pm
- Forum: Secondary Level
- Topic: n divides 2^(n-1)+3^(n-1)
- Replies: 8
- Views: 5638
Re: n divides 2^(n-1)+3^(n-1)
Canceling the powers we get $2\equiv3(mod n)$Substracting 2 gives us $0\equiv1(mod n)$
Am I making a mistake?
Am I making a mistake?
- Fri Jan 31, 2014 9:38 am
- Forum: Secondary Level
- Topic: Nice Equation
- Replies: 4
- Views: 4180
Re: Nice Equation
You should google it.
- Fri Jan 31, 2014 9:34 am
- Forum: Secondary Level
- Topic: n divides 2^(n-1)+3^(n-1)
- Replies: 8
- Views: 5638
Re: n divides 2^(n-1)+3^(n-1)
Check the new one.Thanks for informing the mistake.
- Thu Jan 30, 2014 10:55 am
- Forum: Secondary Level
- Topic: n divides 2^(n-1)+3^(n-1)
- Replies: 8
- Views: 5638
Re: n divides 2^(n-1)+3^(n-1)
$2^{n-1}+3^{n-1}\equiv0(mod n)$
Multiplying $2^{n-1}-3^{n-1}$ in both sides,
$2^{2n-2}-3^{2n-2}\equiv0(mod n)$
$2^{2n-2}\equiv3^{2n-2}(mod n)$
But they are co-prime.So $n$ can only be $1$
Multiplying $2^{n-1}-3^{n-1}$ in both sides,
$2^{2n-2}-3^{2n-2}\equiv0(mod n)$
$2^{2n-2}\equiv3^{2n-2}(mod n)$
But they are co-prime.So $n$ can only be $1$
- Wed Jan 29, 2014 10:28 pm
- Forum: Junior Level
- Topic: I need help
- Replies: 1
- Views: 2644
I need help
I can't solve this one.
Given the value of $a$ and $b$,where $AA'CBB'$ is a thread, is there any formula such that
$x=f(a,b)$?
Sorry I am a little amateur in paint.
Given the value of $a$ and $b$,where $AA'CBB'$ is a thread, is there any formula such that
$x=f(a,b)$?
Sorry I am a little amateur in paint.
- Tue Jan 28, 2014 5:20 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Junior 2011/9
- Replies: 3
- Views: 3594
Re: BdMO National Junior 2011/9
The greatest one or the smallest one?
- Tue Jan 28, 2014 4:50 pm
- Forum: Junior Level
- Topic: Use just logic
- Replies: 5
- Views: 4684
Re: Use just logic
what if $n=1$?nafistiham wrote:if $n$ is prime, take $p=n$ if not, take $p$ as one of $n$'s prime factor.
- Mon Jan 27, 2014 9:09 pm
- Forum: Junior Level
- Topic: Good numbers [self-made]
- Replies: 3
- Views: 3583
Re: Good numbers [self-made]
$\sum_{n=8}^{13}$ $ ^{8}P_n+ ^{13}P_5$
- Mon Jan 27, 2014 8:48 pm
- Forum: Junior Level
- Topic: 3 variables
- Replies: 1
- Views: 2343
3 variables
if,
$a+b+c=3$
$ab+bc+ca=3$
$abc=1$
Prove that $a=b=c=1$
$a+b+c=3$
$ab+bc+ca=3$
$abc=1$
Prove that $a=b=c=1$