## Search found 461 matches

- Tue Jan 29, 2013 4:54 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO H.Sec 2010. Problem 10
- Replies:
**2** - Views:
**2590**

### Re: BdMO H.Sec 2010. Problem 10

Solution: Note that $min\{a_i\}\in\{a_1,a_n\}$ and all are distinct. Let the rightmost point be $R$ Case:1 $min\{a_i\}=a_n$ Then first jump $a_{n-1}$ second jump $a_{n-2}$ ... ... $i'th$ jump $a_{n-i}$ (Where $a_0=a_n$) ...... We'll prove that this process works. After $i'th$ jump (for $i<n$), the d...

- Thu Jan 17, 2013 11:38 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies:
**184** - Views:
**64082**

### Re: IMO Marathon

Sorry to everyone for skipping without explanation . Post a problem now (Please)...

- Thu Jan 17, 2013 11:37 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58704**

### Re: Secondary and Higher Secondary Marathon

Which part?Reza_raj wrote:Can you please explain this!

I don't understand this!

@Tahmid, মোটামুটি ৪ মাস পর এই বছরের সমস্যা সমাধান করা শুরু করলাম। নেশার মত লাগতাসে। নেশা...... চেষ্টা করব পরে পোস্ট করার (সমাধান করতে পারলে)

- Thu Jan 17, 2013 6:47 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies:
**184** - Views:
**64082**

### Re: IMO Marathon

Problem 17: Solution Let $BC\cap AD=O$ then given condition implies $O,K,L$ are collinear. Given conditions also implies $BC$ is common tangent to circles $ABP,CQD$. Note that a homothety with center $O$ sends circles $ABP$ to circle $DQC$. Let $KL\cap \odot ABP =\{P,H\}$ and $KL \cap \odot \{G,Q\}$...

- Thu Jan 17, 2013 5:54 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58704**

### Re: Secondary and Higher Secondary Marathon

Solution: As, $AB||PT$, $P$ is the midpoint of minor arc $BC$ and using cyclic property : $BP=CP=AT$ and so $AP||CT$ (Note that $ABPT,APCT$ cyclic trapezium and the two non-parallel sides of a cyclic trapezium are equal). Similarly in trapezium $APCT$, $CS=TS$ Now $CS=PR \Leftrightarrow PR=ST \Leftr...

- Thu Jan 17, 2013 3:01 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58704**

### Re: Secondary and Higher Secondary Marathon

$\boxed {24}$ Let $N={1,2,3,...,2012}$. A $3$ element subset $S$ of $N$ is called $4$-splittable if there is an $n\in (N-S)$ such that $S\bigcup {n}$ can be partitioned into two sets such that the sum of each set is the same. How many $3$ element subsets of $N$ is non-$4$-splittable? Solution: We'l...

- Thu Jan 17, 2013 1:24 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies:
**184** - Views:
**64082**

### Re: IMO Marathon

Problem $16$: Let $ABC$ be an acute triangle. $(O)$ is circumcircle of $\triangle ABC$. $D$ is on arc $BC$ not containing $A$. Line $\ell$ moves through $H$ ($H$ is the orthocenter of $\triangle ABC$) cuts $\odot ABH,\odot ACH$ again at $M,N$ respectively. (a). Find $\ell$ such that the area of $\t...

- Wed Jan 16, 2013 10:32 pm
- Forum: Divisional Math Olympiad
- Topic: Some problems of last year divisionals, I need help for
- Replies:
**36** - Views:
**12074**

### Re: Some problems of last year divisionals, I need hel for

$5.$ $AB = 9,$ $AC = 5,$ $BC = 6$ in triangle $ABC$ and the angular bisectors of the three angles are $AD, BF$ and $CE$. Now there is a point in the interior from which the distances of $D, E$ and $F$ are equal. Let this distance be $a$. There’s also another point from which the distances of $A, B$...

- Wed Jan 16, 2013 10:20 pm
- Forum: Divisional Math Olympiad
- Topic: Some problems of last year divisionals, I need help for
- Replies:
**36** - Views:
**12074**

### Re: Some problems of last year divisionals, I need hel for

For problem 5 I don't know why but I have a strong feeling that what they wanted to define (D,E,F) are touch points of incircle of $\triangle ABC$. Otherwise the calculation will be painful. @Sourav vaia,they told us that $AD,BE,CF$ are angular bisectors,so $D,E,F$ can't be the touch points. :? And...

- Wed Jan 16, 2013 9:51 pm
- Forum: Divisional Math Olympiad
- Topic: Some problems of last year divisionals, I need help for
- Replies:
**36** - Views:
**12074**

### Re: Some problems of last year divisionals, I need hel for

For problem 5

I don't know why but I have a strong feeling that what they wanted to define (D,E,F) are touch points of incircle of $\triangle ABC$. Otherwise the calculation will be painful.

I don't know why but I have a strong feeling that what they wanted to define (D,E,F) are touch points of incircle of $\triangle ABC$. Otherwise the calculation will be painful.