LetHbe a Hopf algebra in a rigid symmetric monoidal categoryCthen the evaluation map τis a convolution-invertible skew pairing. In the previous paper, we constructed a Hopf algebraD(H)=H⋈rH*copinC. In this paper, we first show thatD(H) is a quasitriangular Hopf algebra inC. Next, letHbe an ordinary triangular finite-dimensional Hopf algebra. Then one can form quasitriangular Hopf algebrasB(H,H)andB(H,D(H))(in a rigid braided monoidal category) by Majid’s method associated to the ordinary Hopf algebra mapsH→HandiHH→D(H), whereD(H)is the Drin-fePd quantum double. We show thatD(B(H,H))andB(H,D(H))are isomorphic Hopf algebras in the braided monoidal category.