Altitudes AD and BE of an acute triangle ABC intersect at H. Let P=E be the point of tangency of the circle with radius HE centred at H with its tangent line going through point C, and let Q=E be the point of tangency of the circle with radius BE centred at B with its tangent line going through C. Prove that the points D,P and Q are collinear.
geometrycollinearorthocenter