+58 Problem: Let ABC be a triangle with circumcenter O, orthocenter H, altitude AD, and median AM. THe line through H perpendicular to AM meets AM, BC at P, Q, respectively. Lines OA and OD meet the circumcircle of BOC again at T, R, respectively, and S is the foot from A to TH. Show that P, Q, R, S are concyclic.
So I don't really know how to start ont his problem and I am pretty sure angle QSP=angle QRP=90, so my goal is to show that, does anyone have any hints or solutions so this problem? Thanks, also I prefer non advanced topics like complex numbers, inversion, barycentrics.
