Y by MathLuis, mpcnotnpc, JollyEggsBanana, Rounak_iitr
Let
be a triangle with incenter
, and let
be a point on side
. Points
and
are chosen on lines
and
respectively such that
is a parallelogram. Points
and
are chosen on side
such that
and
are the angle bisectors of angles
and
respectively. Let
be the circle tangent to segment
, the extension of
past
, and the extension of
past
. Prove that
is tangent to the circumcircle of triangle
.























