AoPS Academy
[/quote]
, do not answer with "
is a solution" only. Either you post any kind of proof or at least something unexpected (like "
is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
and 
be the circumcircle and the circumcentre of an acute-angled triangle 
with 
. The angle bisector of 
intersects at 
. Let 
be the circle with diameter 
. The angle bisectors of 
and 
intersect at points 
and 
respectively. The point 
is chosen on the line 
so that 
. Prove that 
. be an acute triangle with orthocentre 
, and let 
be the midpoint of 
. The point 
on 
is such that 
is an altitude of the triangle . Let 
be the reflection of in . The orthogonal projections of onto the lines 
, and 
are , 
and , respectively. Let 
be the point such that the circumcentre of triangle 
is the midpoint of the segment 
. lies on the segment 
.
and 
. But right answer is only . Should it be reported somewhere in Aops?
, such that 
a grid of 9*9, we choose a little square in of this grid three times, we can choose three times the same.
be positive reals, s.t 
, prove that :
and 
is closest to which integer?
and 
,
.
.
