## ISL 2003

Discussion on International Mathematical Olympiad (IMO)
shehab ahmed
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Joined: Tue Mar 20, 2012 12:52 am

### ISL 2003

Three distinct points $A,B,C$ are fixed on a line in this order.Denote by P the intersection of the tangents to a circle at $A$ and $C$ where the centre of the circle doesn't lie on the line $AC$.Suppose, $Q$ is intersection point of the segment $PB$ and the circle.Prove that the intersection of the bisector of $\angle AQC$ and the line $AC$ doesn't depend on the choice of the circle.
Last edited by sourav das on Mon Apr 09, 2012 8:30 pm, edited 1 time in total.
Reason: Latexed

*Mahi*
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### Re: ISL 2003

This has quite the same main idea like this year's APMO 4.

Use $L^AT_EX$, It makes our work a lot easier!

shehab ahmed
Posts: 66
Joined: Tue Mar 20, 2012 12:52 am

### Re: ISL 2003

Can u please send me a msg about the question of APMO 4?I have forgot the question

*Mahi*
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### Re: ISL 2003

APMO questions are published in the official site, and so we have no problem to discuss them publicly.
Here is the link to APMO official site - http://www.mmjp.or.jp/competitions/APMO/ . You can collect the questions from there.

Use $L^AT_EX$, It makes our work a lot easier!

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### Re: ISL 2003

Hint:

*Mahi*
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### Re: ISL 2003

Use $L^AT_EX$, It makes our work a lot easier!

Posts: 217
Joined: Thu Oct 27, 2011 11:04 am
Location: mymensingh

### Re: ISL 2003

after using this kind of lemma,this problem doesn't seem to be crux.

Posts: 217
Joined: Thu Oct 27, 2011 11:04 am
Location: mymensingh

### Re: ISL 2003

my solution:
Mahi,what did u mean by basic algebra?

*Mahi*
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### Re: ISL 2003

I meant
Do not be afraid, it is not complex
Use $L^AT_EX$, It makes our work a lot easier!