Search found 86 matches

by Kazi_Zareer
Mon Jan 30, 2017 10:42 pm
Forum: National Math Olympiad (BdMO)
Topic: BDMO NATIONAL JUNIOR 2014/10
Replies: 2
Views: 665

Re: BDMO NATIONAL JUNIOR 2014/10

Hint:
Pigeonhole Principle
by Kazi_Zareer
Mon Jan 30, 2017 8:58 am
Forum: Geometry
Topic: USAMO (GEOMETRY) 1995
Replies: 1
Views: 446

USAMO (GEOMETRY) 1995

Given a nonisosceles, nonright triangle $ABC,$ let $O$ denote the center of its circumscribed circle, and let $A_1, B_1,$ and $C_1$ be the midpoints of sides $BC, CA,$ and $AB,$ respectively. Point $A_2$ is located on the ray $OA_1$ so that $\triangle OAA_1$ is similar to $\triangle OA_2A$. Points $...
by Kazi_Zareer
Mon Jan 30, 2017 2:46 am
Forum: Divisional Math Olympiad
Topic: Divisional MO 2015
Replies: 4
Views: 886

Re: Divisional MO 2015

See, $9800 = 2^3 \times 5^2 \times 7^2$ Let the two numbers will be $p = 2^a \times 5^b \times 7^c$ and $q = 2^x \times 5^y \times 7^z$. Now consider the pairs of $(a,x)$ which are possible: $(0,3), (1,3),(2,3),(3,3), (3,0), (3,1), (3,2),(1,2),(2,1)$ , numbers of pairs is $9$. Again, similarly the ...
by Kazi_Zareer
Wed Jan 25, 2017 1:58 am
Forum: Junior Level
Topic: BDMO National Junior 2016/6
Replies: 9
Views: 1868

Re: BDMO National Junior 2016/6

$w+x+y+z=106$
by Kazi_Zareer
Tue Jan 24, 2017 8:16 pm
Forum: National Math Olympiad (BdMO)
Topic: National BDMO Secondary P8
Replies: 4
Views: 1143

Re: National BDMO Secondary P8

I solved by using angle bisector theorem, stewart's theorem, power of the point, law of cosines etc. I think I just messed up but got an answer $AF^2 = 900/19$. So, $m + n = 900 + 19 = 919$

Anyone?
by Kazi_Zareer
Tue Jan 24, 2017 8:09 pm
Forum: National Math Olympiad (BdMO)
Topic: National BDMO Secondary P8
Replies: 4
Views: 1143

National BDMO Secondary P8

$\triangle ABC$ is inscribed in circle $\omega$ with $AB = 5$, $BC = 7$, $AC = 3$. The bisector of $\angle A$ meets side $BC$ at $D$ and circle $\omega$ at a second point $E$. Let $\gamma$ be the circle with diameter $DE$. Circles $\omega$ and $\gamma$ meet at $E$ and at a second point $F$. Then $AF...
by Kazi_Zareer
Mon Jan 23, 2017 2:06 pm
Forum: Junior Level
Topic: BDMO 2013 QUE-9
Replies: 5
Views: 1351

Re: BDMO 2013 QUE-9

Is ther any problem here? We assume two integers: (a,b) where, a=x×y and, b=y×z, such that: gcd(x,z)=1 and y is the GCD of these two integers. So, the sum is: (a+b)=(x×y)+(y×z)=y(x+z)=5460 and, differnece: (a-b)=(x×y)-(y×z)=y(x-z) So, gcd(a,b)=y and, lcm=(a,b)=x×y×z. Then, lcm(a,b)/gcd(a,b) = 36/1 ...
by Kazi_Zareer
Mon Jan 23, 2017 2:02 pm
Forum: Higher Secondary Level
Topic: need a book
Replies: 5
Views: 1394

Re: need a book

Feel free to call Ayub vai (Ayub Sarkar), Phone No. $ 01191385551 $