## Search found 138 matches

- Sun Mar 02, 2014 5:11 pm
- Forum: Geometry
- Topic: Triangle Inside a Square
- Replies:
**1** - Views:
**1453**

### Triangle Inside a Square

$ABCD$ is a square where $AB=4.$ $P$ is a point inside the square such that $\angle PAB = \angle PBA = 15^\circ.$ $E$ and $F$ are the midpoints of $AD$ and $BC$ respectively. $EF$ intersects $PD$ and $PC$ at points $M$ and $N$ respectively. $Q$ is a point inside the quadrilateral $MNCD$ such that $\...

- Sat Feb 08, 2014 6:56 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Junior 5
- Replies:
**5** - Views:
**2989**

### Re: BdMO National 2012: Junior 5

I could solve the 1st part only....can anyone explain the another one..... Brother please show your ans of 1st part :| 1st part ACB%2030.jpg In equilateral triangle $\triangle DEF$, $\angle DFE = \angle DEF = \angle EDF = 60^\circ$ $\angle DFE =\angle CFG = 60^\circ$ $\angle ACB = 90^\circ - \angle...

- Tue Oct 15, 2013 12:43 pm
- Forum: Computer Science
- Topic: Font Size in C
- Replies:
**2** - Views:
**4273**

### Font Size in C

How can I change font size in C ?

- Wed Aug 28, 2013 8:36 pm
- Forum: Junior Level
- Topic: Italian MO 2002#P1
- Replies:
**5** - Views:
**2367**

### Re: Italian MO 2002#P1

$34 \times (a+b+c) = 100a+10b+c$

$\Rightarrow 66a-24b-33c = 0$

$\Rightarrow 11 \times (2a-c) = 8b$

$8b$ will be divisible by $11$ if $b=0$.

Now, $11 \times (2a-c)=0$

$\Rightarrow 2a = c$

So the numbers are $102,204,306,408$.

$\Rightarrow 66a-24b-33c = 0$

$\Rightarrow 11 \times (2a-c) = 8b$

$8b$ will be divisible by $11$ if $b=0$.

Now, $11 \times (2a-c)=0$

$\Rightarrow 2a = c$

So the numbers are $102,204,306,408$.

- Sat Aug 10, 2013 2:26 pm
- Forum: Computer Science
- Topic: Count The Number Of Solutions
- Replies:
**2** - Views:
**4974**

### Count The Number Of Solutions

Suppose, I want to find the number of solutions of this equation $a+b+c+d=7$ ; where $a,b,c,d$ are natural numbers. To find the solutions I wrote the following code. #include <stdio.h> int main () { int a,b,c,d,n; for(a=1;a>=0 && a<=7;a++) {for(b=1;b>=0 && b<=7;b++) {for(c=1;c>=0 && c<=7;c++) {for(d...

### Re: algebra

When $x=1$ and $y=1$ , $z+t=5$ has $4$ solutions. Keeping $x=1$ fixed, $+1$ the value of $y$ gradually. Then $z+t$ will have $3,2$ and $1$ solutions for $y=2,3,4$ respectively. So keeping $x=1$ fixed, we get $4+3+2+1=10$ solutions. Keeping $x=2$ fixed, we get $(10-4)=6$ solutions. [4 solutions out. ...

- Tue Mar 05, 2013 12:08 am
- Forum: Social Lounge
- Topic: APMO
- Replies:
**2** - Views:
**2316**

### APMO

Today I saw an add on APMO. Will someone tell me in detail about it?

- Mon Feb 25, 2013 4:46 pm
- Forum: Number Theory
- Topic: Perfect Square
- Replies:
**6** - Views:
**2095**

### Re: Perfect Square

One more thing I want to say-

It can have more solutions except those 3.

It can have more solutions except those 3.

- Mon Feb 25, 2013 4:42 pm
- Forum: Number Theory
- Topic: Perfect Square
- Replies:
**6** - Views:
**2095**

### Re: Perfect Square

:( Sorry for doing mistake in haste. $d=gcd(y+3,y-3) = 2 or 6$ When d=2, Let $(y+3)=2a$,$(y-3)=2b$ ; where $a,b$ are relatively prime. And $x=2k$ $16k^3 = 4ab$ $4k^3 = ab$ As $a,b$ are relatively prime. each divisor of k must enter one of them. $k=uv$, $(a=4u^3,b=v^3)$ or $(a=u^3,b=4v^3)$ $4u^3-v^3=...

- Sun Feb 24, 2013 2:26 pm
- Forum: Secondary Level
- Topic: Find angle OAC
- Replies:
**0** - Views:
**1087**

### Find angle OAC

O is a point inside $\triangle ABC$ such that $\angle OBA = \angle OBC = 20°$ , $\angle OCB = 10°$ and $\angle OCA = 30°$.

$\angle OAC = ?$

$\angle OAC = ?$