passing through 
at point 
.
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
Given a right triangle 
with 
. On its hypotenuse 
is arbitrary mark the point
. The point 
is symmetric to the point 
wrt 
. Let the lines 
and 
intersect at points 
and 
respectively. Denote by 
the foot of the perpendicular from the point on the line (
), and let 
be the intersection point of lines 
and 
. Prove that is the center of the circle inscribed in the triangle 
.
with 
. On its hypotenuse 
is arbitrary mark the point
. The point 
is symmetric to the point 
wrt 
. Let the lines 
and 
intersect at points 
and 
respectively. Denote by 
the foot of the perpendicular from the point on the line (
), and let 
be the intersection point of lines 
and 
. Prove that is the center of the circle inscribed in the triangle 
.This post has been edited 2 times. Last edited by parmenides51, Jun 21, 2022, 3:00 AM
