be tangent to the side 
at the point 
.
on 
and 
on 
and 
lies on the circumcircle of triangle 
be the second intersection of 
and 
,
be a transversal of 
be intersections of 
with 
be a tangent line of 
is cyclic
be positive integers such that 
and 
.
.
.
are the midpoints of 
respectively. 
,
is symmetric to 
.
be the incenter and tangent of angles 
respectively. Prove that 
have a common point
and 
.
specifies the greatest common divisor of 
and 
.
be real numbers so that 
and 
Show that
and 
such that:
Y by Mango247
The circle 
is circumscribed around an acute-angled triangle 
. The tangent to the circle at the point 
meets the line 
at the point 
. Point 
is the midpoint of segment 
. Line 
intersects for the second time circle at point 
, and line 
intersects the circle for the second time at point 
. Prove that lines 
and are parallel.
is circumscribed around an acute-angled triangle 
. The tangent to the circle at the point 
meets the line 
at the point 
. Point 
is the midpoint of segment 
. Line 
intersects for the second time circle at point 
, and line 
intersects the circle for the second time at point 
. Prove that lines 
and are parallel.This post has been edited 1 time. Last edited by parmenides51, Jan 4, 2021, 7:45 AM
