such that:
with all 
is real number
be a triangle, and let 
,
,
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
We consider 
and 
two circles that intersect at points 
and 
. Let 
and 
be points on the circle and 
and 
points on the circle so that the lines 
and 
intersect at and the lines 
and 
intersect at . Denote 
and 
the intersections of lines 
and 
and of lines 
and 
, respectively. Show that 
is a parallelogram.
and 
two circles that intersect at points 
and 
. Let 
and 
be points on the circle and 
and 
points on the circle so that the lines 
and 
intersect at and the lines 
and 
intersect at . Denote 
and 
the intersections of lines 
and 
and of lines 
and 
, respectively. Show that 
is a parallelogram.
,
,
