such that 
.
.
and 
be the feet of the altitudes from 
to 
to 
respectively.
and 
as the reflections of 
and 
be the circumcircle of 
.
the second intersection of line 
with 
the intersection of ray 
with 
is the circumcenter of 
can be inscribed within a circle.
of positive integers satisfying the following two conditions:
,
is in 
,
and 
;
such that 
is not divisible by 
.
?
Y by doxuanlong15052000, Davi-8191, Adventure10
Let 
be an acute-angled triangle, with 
. Let 
be the midpoint of side 
, and 
be the feet of the altitude from 
respectively. Denote by 
the midpoints of segments 
, respectively. Suppose 
is a point on the line 
such that 
.
Prove that
.
be an acute-angled triangle, with 
. Let 
be the midpoint of side 
, and 
be the feet of the altitude from 
respectively. Denote by 
the midpoints of segments 
, respectively. Suppose 
is a point on the line 
such that 
.Prove that
.
r
. we know 
t
,
,
lying on the unit circle with circumcenter 
.
,
,
.
,
.
.
.
,
.
,
