IMO(1995-1) Collinearity Of AM, DN and XY

Discussion on International Mathematical Olympiad (IMO)
Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm

IMO(1995-1) Collinearity Of AM, DN and XY

Let $A, B, C,$ and $D$ be distinct points on a line, in that order. The circles
with diameters $AC$ and $BD$ intersect at $X$ and $Y$ . $O$ is an arbitrary point
on the line $XY$ but not on $AD$. $CO$ intersects the circle with diameter
$AC$ again at $M$, and $BO$ intersects the other circle again at $N$. Prove that
the lines $AM, DN,$ and $XY$ are concurrent.
Last edited by Labib on Tue Jan 31, 2012 11:40 pm, edited 1 time in total.
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Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm

Re: IMO(1995-1) Colliniarity Of AM, DN and XY

Here's my solution::
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bristy1588
Posts: 92
Joined: Sun Jun 19, 2011 10:31 am

Re: IMO(1995-1) Collinearity Of AM, DN and XY

my solution might be wrong, if it is, i request people to correct it:
Hopefully, proved
Bristy Sikder