Points D and E are taken on [BC] and [AC] of acute angled triangle ABC such that BD and CE are angle bisectors. Projections of D onto BC and BA are P and Q, projections of E onto CA and CB are R and S. Let AP∩CQ=X, AS∩BR=Y and BX∩CY=Z. Show that AZ⊥BC. geometrygeometry proposedangle bisectorZ -orthocenter