Let ABC be a right triangle at A and altitude AH. Draw a circle with center A and radius AH. From H draw HD perpendicular to AB at D and HE perpendicular to AC at A a) prove A,D,H,E are on the same circle b) HD and HE intersect at circle center A at P respectively and Q. prove that D is the midpoint of HP and the three points P,A,Q are collinear