IMO(1995-1) Collinearity Of AM, DN and XY
Posted: Tue Jan 31, 2012 4:24 pm
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.
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.