Y by ike.chen, Adventure10, Rounak_iitr
Let
be a scalene triangle with circumcircle
. Let
be the midpoint of
. A variable point
is selected in the line segment
. The circumcircles of triangles
and
intersect
again at points
and
, respectively. The lines
and
intersect (a second time) the circumcircles to triangles
and
at
and
, respectively. Prove that as
varies, the circumcircle of
passes through a fixed point
distinct from
.




















