Let ABC a triangle with circumcircle Γ and R a point inside ABC such that ∠ABR=∠RBC. Let Γ1 and Γ2 the circumcircles of triangles ARB and CRB respectly. The parallel to AC that pass through R, intersect Γ in D and E, with D on the same side of BR that A and E on the same side of BR that C. AD intersect Γ1 in P and CE intersect Γ2 in Q. Prove that APQC is cyclic if and only if AB=BC geometrycircumcircleparallel