2008 IMO Problems/Problem 1
Problem 1
An acute-angled triangle has orthocentre
. The circle passing through
with centre the midpoint of
intersects the line
at
and
. Similarly, the circle passing through
with centre the midpoint of
intersects the line
at
and
, and the circle passing through
with centre the midpoint of
intersects the line
at
and
. Show that
,
,
,
,
,
lie on a circle.