be positive real integer such that 
Prove that
such that 
and 
that verify the following equation for all 
:
is a prime number
.
be the feet of the altitudes from 
to 
respectively. Let 
be the midpoint of 
.
be the circle with diameter 
.
be the intersection of 
and 
.
be the orthocenter of 
and 
be the lines through 
respectively. Let 
be the intersection of 
and 
.
be the intersection of 
and 
.
be the line through 
and let 
be the reflection of 
is tangent to 
.
Y by
Let 
and 
be the points of tangency of the incircle of the triangle 
with the sides. Let 
be the center of a circle passing through the midpoints of the segments 
and 
. Prove that the centers of the circumscribed and inscribed circle of the triangle and the point are on the same line.
and 
be the points of tangency of the incircle of the triangle 
with the sides. Let 
be the center of a circle passing through the midpoints of the segments 
and 
. Prove that the centers of the circumscribed and inscribed circle of the triangle and the point are on the same line.This post has been edited 1 time. Last edited by parmenides51, Sep 22, 2020, 6:23 PM
