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.

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

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

Last edited by Labib on Tue Jan 31, 2012 11:40 pm, edited 1 time in total.

Please

**Install $L^AT_EX$ fonts**in your PC for better looking equations,**Learn****how to write equations**, and**don't forget**to read**Forum Guide and Rules.****"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes**### Re: IMO(1995-1) Colliniarity Of AM, DN and XY

Here's my solution::

Please

**Install $L^AT_EX$ fonts**in your PC for better looking equations,**Learn****how to write equations**, and**don't forget**to read**Forum Guide and Rules.****"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes**- 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