be an acute triangle with circumcenter 
.
,
on side 
.
passing through 
at point 
.
and 
be a triangle and 
points in the same plane such that 
,
,
.
is parallel to 
,
is the midpoint of segment 
,
and
meaning 
is the least common multiple of the numbers 
.
such that
for every positive integer 
such that 
for any relatively prime natural numbers 
.
Y by Adventure10, Mango247
Let 
be the incenter of triangle 
. The straight lines 
and 
intersect the outcircle 
of triangle at points 
and 
respectively. Let 
be the diameter of and 
be the intersection point of 
and 
. Prove that 
.
(T. Tymoshkevych, Kyiv)
be the incenter of triangle 
. The straight lines 
and 
intersect the outcircle 
of triangle at points 
and 
respectively. Let 
be the diameter of and 
be the intersection point of 
and 
. Prove that 
.(T. Tymoshkevych, Kyiv)
