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Given a cyclic quadrilateral
with
and
. Lines
and
intersect at
, and lines
and
intersect at
. Let
be the midpoints of sides
, respectively. Let
and
be points on segment
and
, respectively, so that
is the angle bisector of
and
is the angle bisector of
. Prove that
is parallel to
if and only if
divides
into two triangles with equal area.






















