Let ABC be an acute triangle (AB<BC<AC) with circumcircle Γ. Assume there exists X∈AC satisfying AB=BX and AX=BC. Points D,E∈Γ are taken such that ∠ADB<90∘, DA=DB and BC=CE. Let P be the intersection point of AE with the tangent line to Γ at B, and let Q be the intersection point of AB with tangent line to Γ at C. Show that the projection of D onto PQ lies on the circumcircle of △PAB. geometryAZE BMO TSTTSTBMO Shortlist