## Search found 461 matches

Tue Jan 29, 2013 4:54 pm
Topic: BdMO H.Sec 2010. Problem 10
Replies: 2
Views: 1339

### 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
Topic: IMO Marathon
Replies: 184
Views: 23750

### 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: 125
Views: 17621

### Re: Secondary and Higher Secondary Marathon

Reza_raj wrote:Can you please explain this!
I don't understand this!
Which part?
@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
Topic: IMO Marathon
Replies: 184
Views: 23750

### 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: 125
Views: 17621

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 $CS=PR \Leftrightarrow PR=ST \Leftr... Thu Jan 17, 2013 3:01 pm Forum: Higher Secondary Level Topic: Secondary and Higher Secondary Marathon Replies: 125 Views: 17621 ### Re: Secondary and Higher Secondary Marathon$\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: 23750 ### 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
Topic: Some problems of last year divisionals, I need help for
Replies: 36
Views: 3907

### 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
Topic: Some problems of last year divisionals, I need help for
Replies: 36
Views: 3907

### 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
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.