ISL 2003
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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
Reason: Latexed
Re: ISL 2003
This has quite the same main idea like this year's APMO 4.
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Re: ISL 2003
Can u please send me a msg about the question of APMO 4?I have forgot the question
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.
Here is the link to APMO official site - http://www.mmjp.or.jp/competitions/APMO/ . You can collect the questions from there.
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
- zadid xcalibured
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Re: ISL 2003
Hint:
Re: ISL 2003
zadid xcalibured wrote:Hint:
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
- zadid xcalibured
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Re: ISL 2003
after using this kind of lemma,this problem doesn't seem to be crux.
- zadid xcalibured
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Re: ISL 2003
my solution:
Mahi,what did u mean by basic algebra?
Re: ISL 2003
I meant
Do not be afraid, it is not complex
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
- zadid xcalibured
- Posts:217
- Joined:Thu Oct 27, 2011 11:04 am
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Re: ISL 2003
কমপ্লেক্স হলে ভয় পাওয়ার কি আছে ?