## Search found 65 matches

Wed Mar 07, 2018 6:28 pm
Topic: BdMO National Higher Secondary 2014/6
Replies: 6
Views: 2191

### Re: BdMO National Higher Secondary 2014/6

samiul_samin wrote:
Mon Mar 05, 2018 11:54 pm
Absur Khan Siam wrote:
Mon Mar 05, 2018 11:27 pm
Sorry, the solution above is wrong. I will edit it as soon as possible.(as I can't delete it now)
Is my solution also wrong?
Not yours, my one was wrong.(now edited)
Mon Mar 05, 2018 11:27 pm
Topic: BdMO National Higher Secondary 2014/6
Replies: 6
Views: 2191

### Re: BdMO National Higher Secondary 2014/6

Sorry, the solution above is wrong. I will edit it as soon as possible.(as I can't delete it now)
UPD: : solution edited.
Mon Mar 05, 2018 11:16 pm
Topic: BdMO National Higher Secondary 2014/6
Replies: 6
Views: 2191

### Re: BdMO National Higher Secondary 2014/6

Let us construct a directed graph $T$ consisting $n$ nodes where each node represents a player. An edge $x \rightarrow y$ represent player $x$ has lost $y$. Thus, this graph consists of $\binom{n}{2}$ edges. "The players can be labeled $1,2,.......,n$ so that $i$ beats $i+1$" is equivalent to "The g...
Mon Mar 05, 2018 10:52 pm
Topic: BDMO 2017 National round Secondary 5
Replies: 15
Views: 5838

### Re: BDMO 2017 National round Secondary 5

Tasnood wrote:
Mon Mar 05, 2018 10:34 pm
Sorry for Interrupt. My answer was same of #Nahin but this solution is new to me.
How can we find the radius of two circles same?
$AC = AB$ , radius of the $\widehat{BC}$
$BC = AB$ , radius of the $\widehat{AB}$

Thus, $AC = BC$
Sat Feb 10, 2018 10:59 pm
Forum: Secondary Level
Topic: Find Formula for Sequence
Replies: 2
Views: 1249

### Re: Find Formula for Sequence

It is a linear recurrence relation.You can derive the formula of $a_n$ by solving this recurrence relation.
Sun Feb 04, 2018 11:17 pm
Forum: Geometry
Topic: EGMO 2013/1
Replies: 2
Views: 7840

Applying Apollonius's theorem to $\triangle ABD$ , $AB^2 + AD^2 = 2AC^2 + 2BC^2 \cdots (i)$ Applying Stuart's theorem to $\triangle BCE$ , $CE(AB^2 + AC.CE) = BE^2.AC + BC^2.AE \cdots (ii) \Rightarrow 3AB^2 + 6AC^2 = AD^2 + 2BC^2$ $(i) + (ii)$ $\Rightarrow 4AB^2 + 4AC^2 = 4BC^2 \Rightarrow AB^2 + A... Sun Feb 04, 2018 11:08 pm Forum: Geometry Topic: EGMO 2013/1 Replies: 2 Views: 7840 ### EGMO 2013/1 The side$BC$of$\triangle ABC$is extended beyond$C$to$D$so that$CD = BC$.The side$CA$is extended beyond$A$to$E$so that$AE = 2CA$. Prove that if$AD = BE$, then$\triangle ABC$is right-angled. Sun Feb 04, 2018 12:34 pm Forum: National Math Olympiad (BdMO) Topic: BDMO 2017 National round Secondary 1 Replies: 19 Views: 8171 ### Re: BDMO 2017 National round Secondary 1 My solution may be wrong.But the$20$cases yield to a result that both team have a probability of$\frac{1}{2}$to win the series. Sat Feb 03, 2018 11:16 pm Forum: National Math Olympiad (BdMO) Topic: BDMO 2017 National round Secondary 1 Replies: 19 Views: 8171 ### Re: BDMO 2017 National round Secondary 1 Here are the list of all possibilities of the result of the game(Denoting$W$and$L$are the win and lose of Bangladesh):$WWWLLLLWWWWLWWWWLWWLLLLWLLLLWLWWLLWWLWLWWLLWWLWWLWLWLWWLLWWWWWLLLWLWLLWLLWLLWWLLLWLWLLLWWL$Hence there are$20\$ differ...
Sat Feb 03, 2018 12:40 pm