Search found 81 matches
- Thu Oct 27, 2016 12:30 pm
- Forum: Secondary Level
- Topic: why I'm getting 2 answers contrary to each other
- Replies: 4
- Views: 4951
Re: why I'm getting 2 answers contrary to each other
Perhaps, nobody is getting my question.In the attachment you can see I got two results but they are contrary.The theorem is sum of any two sides of a triangle is greater than twice of the median drawn to the third side.Firstly, I proved that.It was AB+AC>2AD.However, interesting thing was in the se...
- Thu Oct 27, 2016 12:14 pm
- Forum: Secondary Level
- Topic: why I'm getting 2 answers contrary to each other
- Replies: 4
- Views: 4951
Re: why I'm getting 2 answers contrary to each other
Perhaps, nobody is getting my question.In the attachment you can see I got two results but they are contrary.The theorem is sum of any two sides of a triangle is greater than twice of the median drawn to the third side.Firstly, I proved that.It was AB+AC>2AD.However, interesting thing was in the se...
- Sat Aug 27, 2016 4:04 pm
- Forum: Number Theory
- Topic: India TST 2014
- Replies: 3
- Views: 3534
Re: India TST 2014
Yeah , that's easy to see after some experiment. But u have to show your whole own solution.
Hint:
Hint:
- Sun Aug 21, 2016 8:14 pm
- Forum: Number Theory
- Topic: gcd and divisibility
- Replies: 5
- Views: 4004
Re: gcd and divisibility
I got that divisibility part that 9 is the factor of k but I I didn't get the probability part.if u could interpret how to determine the probability It would be percieved...thanx OK . If $ 9|k$, then $k$ is divided by $9$ only when it is a multiple of $9$. Then u will get $ k$ as a multiple of $9$ ...
- Sun Aug 21, 2016 2:41 am
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies: 184
- Views: 112067
Re: IMO Marathon
$\boxed{\textbf{Problem 45}}$ The isosceles triangle $\triangle ABC$, with $AB=AC$, is inscribed in the circle $\omega$. Let $P$ be a variable point on the arc $\stackrel{\frown}{BC}$ that does not contain $A$, and let $I_B$ and $I_C$ denote the incenters of triangles $\triangle ABP$ and $\triangle...
- Sun Aug 21, 2016 12:55 am
- Forum: Number Theory
- Topic: gcd and divisibility
- Replies: 5
- Views: 4004
Re: gcd and divisibility
The ans is $ \dfrac{1}{ 9} $. It's a very easy problem. Here,By PPF, $ 864 $ = $ 2^5 * 3^3 $ . & $ 1944 = 2^3 * 3^5 $ . Here, $ \frac{ 864}{ 1944 } $ = $ \frac{2^2}{3^2} $ =$ \frac{4}{9} $. The probability of a multiple of $ 4 $ is divisibled by $ 9 $ is $ \frac{ 1}{9 } $ ,as $ 4 $ & $ 9 $ are relat...
- Fri Aug 12, 2016 1:07 pm
- Forum: Social Lounge
- Topic: A ques. about geo
- Replies: 2
- Views: 3161
Re: A ques. about geo
Most of the times, you don't need to prove those lemmas, since they are pretty much well known by now. In general, if you are unsure whether you should prove a lemma or not, then just prove it. You have a lot of time in the major contests. Writing up a known proof or two won't hurt, will it? Thanks...
- Mon Aug 08, 2016 5:49 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2016 #3
- Replies: 1
- Views: 6788
Re: APMO 2016 #3
$ OK. $ First we draw a second tangent from P to $ \omega $ named $ PG $ . Here, $ PG||MR||AE $ (it can be showed easily). We let, There is $ P_{\infty} $ on the line $ PG $ . Now, $ PMNP_{\infty} $ is a quadrangle & $ E , F $ are the tangent or contact point of $ MP $ & $ NP_{\infty} $ resp to $ \o...
- Mon Aug 08, 2016 3:49 pm
- Forum: Social Lounge
- Topic: A ques. about geo
- Replies: 2
- Views: 3161
A ques. about geo
Is it permitted to use geometry camp 2009's $ easy $ section lemma for solving geometry problems without proving
- Sun Aug 07, 2016 7:53 pm
- Forum: Number Theory
- Topic: IMO Shortlist 2012 N1
- Replies: 7
- Views: 5437
Re: IMO Shortlist 2012 N1
There is no condition saying $kx^2 \in A$. You have to prove it. (Though the proof is very obvious). $ OK $. if we let $ x=y $ of the condition. Then, a simple manipulation tells us that it is obvious $ (kx^2 \in A) $ for all $ k $ under admissible-set condition . Plugging, $ x=y $ of the definatio...