The result follows by proving $RP=QC$ and showing $\triangle{LCQ}$ and $\triangle{PKC}$ similar

## Search found 217 matches

- Wed Jan 09, 2013 7:49 pm
- Forum: Geometry
- Topic: IMO 2007 Problem 4
- Replies:
**4** - Views:
**8931**

- Sun Jan 06, 2013 6:15 pm
- Forum: Introductions
- Topic: Hello Everybody
- Replies:
**3** - Views:
**2365**

### Re: Hello Everybody

Hello everyone.I am Zadid Hasan from the town of Mymensingh,Bangladesh.I joined this forum on Oct 27,2011.My present favourite color is BLUE.

Btw welcome charityst021.

Tiham,What do you mean your forum?

Having post number too high doesn't make it yours.

Btw welcome charityst021.

Tiham,What do you mean your forum?

Having post number too high doesn't make it yours.

- Fri Jan 04, 2013 10:14 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58748**

### Re: Secondary and Higher Secondary Marathon

Some moderator edit this.

- Thu Jan 03, 2013 2:44 pm
- Forum: Number Theory
- Topic: IMO Shortlist 2007 N1
- Replies:
**2** - Views:
**1273**

### Re: IMO Shortlist 2007 N1

My steps:

- Thu Jan 03, 2013 2:41 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58748**

### Re: Secondary and Higher Secondary Marathon

Here goes another easy one.

Problem $23$:Find all continuous functions from the set of real numbers to itself satisfying $f(x + y) = f(x) + f(y) + f(x)f(y)$.

Problem $23$:Find all continuous functions from the set of real numbers to itself satisfying $f(x + y) = f(x) + f(y) + f(x)f(y)$.

- Thu Jan 03, 2013 3:08 am
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58748**

### Re: Secondary and Higher Secondary Marathon

It seems you folks lack stamina for a marathon.But resting is enough already i suppose.Let the marathon commence again with an easier problem. Problem $22$:Let $CH$ be the altitude of triangle $ABC$ with $∠ACB = 90°$. The bisector of $∠BAC$ intersects $CH$, $CB$ at $P$, $M$ respectively. The bisecto...

- Fri Dec 21, 2012 3:52 am
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58748**

### Re: Secondary and Higher Secondary Marathon

Problem $21$: Determine all positive rationals $x,y,z$ such that $x+y+z$,$xyz$,$\frac{1} {x}+\frac{1} {y}+\frac{1} {z}$ are all integers.

- Fri Dec 21, 2012 12:47 am
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58748**

### Re: Secondary and Higher Secondary Marathon

This sequence must be periodic with period at most $9$.Actually this is periodic with period $6$.So $A(30)=A(6)=77777770000000$

- Wed Dec 19, 2012 11:05 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies:
**127** - Views:
**58748**

### Re: Secondary and Higher Secondary Marathon

Oops.Edited.

- Wed Dec 19, 2012 3:40 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies:
**184** - Views:
**64124**

### Re: IMO Marathon

To revive the marathon here goes a problem.

Problem $14$:Let $a$ and $b$ be positive integers such that $a^n +n$ divides $b^n +n$ for

every positive integer $n$. Show that $a = b$.

Problem $14$:Let $a$ and $b$ be positive integers such that $a^n +n$ divides $b^n +n$ for

every positive integer $n$. Show that $a = b$.