Let Ω denote the circumcircle of ABC.
The tangent to Ω at A meets BC at X.
Let the angle bisectors of ∠AXB meet
AC and AB at E and F
respectively. D is the foot of the angle
bisector from ∠BAC on BC. Let AD
intersect EF at K and Ω again at
L(other than A). Prove that AEDF is
a rhombus and further prove that the
circle defined by triangle KLX passes
through the midpoint of line segment
BC.