A geometry problem by Soumita Hait
Let X be any point on the circumcircle of triangle ABC. Let the altitudes AD, BE, CF meet the circle again at D',E',F' ; if XA', XB', XC' cut BC,CA,AB at P,Q,R. Does the orthocentre of triangle ABC lie on line PQR and what is the relation between the pedal line of X and line PQR?
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