Given is an acute angled triangle ABC with orthocenter H and circumcircle k. Let ω be the circle with diameter AH and P be the point of intersection of ω and k other than A. Assume that BP and CP intersect ω for the second time at points Q and R, respectively. If D is the foot of the altitude from A to BC and S is the point of the intersection of ω and QD, prove that HR=HS. geometryorthocenterJuniorBalkanshortlist