such that
holds for all 
.
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?
Y by anantmudgal09, Adventure10, Mango247
Let the quadrilateral 
be inscribed in a circle with center 
. Suppose that 
and 
are obtuse, and let lines 
and 
intersect at 
. Let 
and 
be the foot of the perpendiculars dropped from to the lines 
and 
respectively. Extend 
to hit at 
, and let 
hit at 
. Finally, let 
be the midpoint of 
. Prove that 
are collinear.
be inscribed in a circle with center 
. Suppose that 
and 
are obtuse, and let lines 
and 
intersect at 
. Let 
and 
be the foot of the perpendiculars dropped from to the lines 
and 
respectively. Extend 
to hit at 
, and let 
hit at 
. Finally, let 
be the midpoint of 
. Prove that 
are collinear.
and let 
be the inverse of 
.
,
.
is a symmedian in 
,
is a median in 
.
