be a cyclic quadrilateral. The point 
is the reflection of 
the intersection of 
and 
is the reflection of 
.
be the reflection of 
.
concyclic.
. Prove that: 
be a point on side 
and ray 
. The circumcircle of triangle 
intersects the circumcircle 
of triangle 
distinct from point 
and 
intersect 
and 
respectively.
such that 
for all real number 
and 
Y by Adventure10
The line parallel to side 
of a right triangle 
intersects sides 
and 
at 
and 
, respectively, so that the 
. Let 
be the intersection point of the segments 
and 
and 
be a point on the segment 
such that 
. The perpendicular line to at point and the bisector of triangle of 
meet at point 
. Find the angle 
.
of a right triangle 
intersects sides 
and 
at 
and 
, respectively, so that the 
. Let 
be the intersection point of the segments 
and 
and 
be a point on the segment 
such that 
. The perpendicular line to at point and the bisector of triangle of 
meet at point 
. Find the angle 
.
