In an acute triangle △ABC, let there be point D on segment AC,E on segment AB such that ∠ADE=∠ABC. Let the bisector of ∠A hit BC at K. Let the foot of the perpendicular from K to DE be P, and the foot of the perpendicular from A to DE be L. Let Q be the midpoint of AL. If the incenter of △ABC lies on the circumcircle of △ADE, prove that P,Q and the incenter of △ADE are collinear. geometryincentercircumcirclecollinearcollinearity