AoPS Academy
where 
is in radians.
be distinct reals such that 
Prove that 
be the altitude and 
be the intersection point of the altitudes of triangle 
. Point 
is symmetric to with respect to 
. The circumcircle of triangle 
intersects at points 
and 
. Prove that 
.
. is located on the diagonal 
, then the parallelogram is a rhombus. a rhombus whenever the circumcenter of the triangle is located on the diagonal ?
.
be a point on 
, and let 
be a line passing through such that
. intersects 
at 
and the circumcircle of triangle 
at 
(
).
and 
are tangent at .
other than a polynomial satisfying
grid if the centres of no four colored squares form a parallelogram.
Prove that
