such that
holds for all 
.
such that:
with all 
is real number
,
,
be collinear points such that 
,
,
.
,
,
are the reflections of 
,
,
,
is a nondegenerate triangle, then its circumcenter lies on the circumcircle of 
be three positive real numbers satisfying 
Prove that
There is a very elegant proof :-D Could anyone think of it?
Y by
Let 
be an acute the triangle with 
. The point 
, located on the side 
, it is the foot of the altitude drawn from the vertex 
, and 
is the orthocenter of the triangle . On the ray 
take a point 
such that 
. The circle circumscribed around the triangle 
intersects the segment 
for second time ar point 
such that the point also lies on the circle circumscribed around the triangle . Prove that line 
passes through the midpoint of the side .
be an acute the triangle with 
. The point 
, located on the side 
, it is the foot of the altitude drawn from the vertex 
, and 
is the orthocenter of the triangle . On the ray 
take a point 
such that 
. The circle circumscribed around the triangle 
intersects the segment 
for second time ar point 
such that the point also lies on the circle circumscribed around the triangle . Prove that line 
passes through the midpoint of the side .This post has been edited 1 time. Last edited by parmenides51, Mar 25, 2021, 7:22 AM
Reason: vertex instead of vertice
Reason: vertex instead of vertice
and 
the foots of the altitudes drawn from 
respectively 
.
.
we deduce that 
.
are collinear where 
is the midpoint of 
