## Search found 86 matches

- Tue Jan 31, 2017 12:14 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO NATIONAL Junior 2016/05
- Replies:
**1** - Views:
**645**

### Re: BDMO NATIONAL Junior 2016/05

Same problem: viewtopic.php?f=13&p=17446#p17446

- Mon Jan 30, 2017 10:42 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO NATIONAL JUNIOR 2014/10
- Replies:
**2** - Views:
**884**

- Mon Jan 30, 2017 8:58 am
- Forum: Geometry
- Topic: USAMO (GEOMETRY) 1995
- Replies:
**1** - Views:
**630**

### 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 $...

- Mon Jan 30, 2017 2:46 am
- Forum: Divisional Math Olympiad
- Topic: Divisional MO 2015
- Replies:
**4** - Views:
**1151**

### 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 ...

- Fri Jan 27, 2017 12:09 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Geometry from bigganchinta
- Replies:
**1** - Views:
**735**

- Wed Jan 25, 2017 1:58 am
- Forum: Junior Level
- Topic: BDMO National Junior 2016/6
- Replies:
**9** - Views:
**2920**

- Tue Jan 24, 2017 8:16 pm
- Forum: National Math Olympiad (BdMO)
- Topic: National BDMO Secondary P8
- Replies:
**4** - Views:
**1498**

- Tue Jan 24, 2017 8:09 pm
- Forum: National Math Olympiad (BdMO)
- Topic: National BDMO Secondary P8
- Replies:
**4** - Views:
**1498**

### 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...

- Mon Jan 23, 2017 2:06 pm
- Forum: Junior Level
- Topic: BDMO 2013 QUE-9
- Replies:
**5** - Views:
**1681**

### 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 ...

- Mon Jan 23, 2017 2:02 pm
- Forum: Higher Secondary Level
- Topic: need a book
- Replies:
**5** - Views:
**2244**

### Re: need a book

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