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?
such that 
and has exactly 
Y by Adventure10, Mango247
Let 
be points in the plane, such that we can draw 
equal circumferences in which the first one passes through 
and 
, the second one passes through and 
, the last one passes through and , and all circumferences share a common point 
.
Show that the radius of each of these circumferences is equal to the circumradius of triangle
, and that is the orthocenter of triangle .
be points in the plane, such that we can draw 
equal circumferences in which the first one passes through 
and 
, the second one passes through and 
, the last one passes through and , and all circumferences share a common point 
.Show that the radius of each of these circumferences is equal to the circumradius of triangle
, and that is the orthocenter of triangle .
