It is given triangle ABC and points P and Q on sides AB and AC, respectively, such that PQ∣∣BC. Let X and Y be intersection points of lines BQ and CP with circumcircle k of triangle APQ, and D and E intersection points of lines AX and AY with side BC. If 2⋅DE=BC, prove that circle k contains intersection point of angle bisector of ∠BAC with BC geometrycircumcircleangle bisector