Let ABC be an acute, non-isosceles triangle inscribed in (O) and BB′, CC′ are altitudes. Denote E,F as the intersections of BB′, CC′ with (O) and D,P,Q are projections of A on BC, CE, BF. Prove that the perpendicular bisectors of PQ bisects two segments AO, BC. geometrybisects segmentperpendicular bisector