In an acute-angled triangle ABC, H be the orthocenter of it and D be any point on the side BC. The points E, F are on the segments AB, AC, respectively, such that the points A, B, D, F and A, C, D, E are cyclic. The segments BF and CE intersect at P. L is a point on HA such that LC is tangent to the circumcircle of triangle PBC at C. BH and CP intersect at X. Prove tha the points D, X, and L lie on the same line.