Let ABC be a triangle whose inscribed circle is ω. Let r1 be the line parallel to BC and tangent to ω, with r1=BC and let r2 be the line parallel to AB and tangent to ω with r2=AB. Suppose that the intersection point of r1 and r2 lies on the circumscribed circle of triangle ABC. Prove that the sidelengths of triangle ABC form an arithmetic progression. geometryincirclecircumcircle