of positive integers with the following property: all of the terms of the sequence 
have a greatest common divisor 
of natural numbers such that
be an acute scalene triangle. Let 
and 
be two distinct interior points of the segment 
such that 
.
and 
are the feet of the perpendiculars from from 
to the lines 
and 
respectively.
and 
are the feet of the perpendiculars from 
to the lines 
and 
intersect on the line 
Y by Adventure10, Mango247, Mango247
The bisector of the angle 
of the triangle 
intersects the side 
at the point 
, and the circumcircle at 
. The points 
and 
are defined similarly. The lines 
and 
intersect at the point 
. Prove that 
is parallel to the side 
, where 
is the center of the inscribed circle.
of the triangle 
intersects the side 
at the point 
, and the circumcircle at 
. The points 
and 
are defined similarly. The lines 
and 
intersect at the point 
. Prove that 
is parallel to the side 
, where 
is the center of the inscribed circle.
be the point at the infinity of the line 
we have 
we get the conclusion
