Abstract: We apply the technique of Karoly Bezdek and Daniel Bezdek to study the billiards in convex bodies, when the length is measured with a (possibly asymmetric) norm. We give elementary proofs of some known results and prove an estimate for the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. (joint work with A. M. Balitskiy, R. N. Karasev, and A. Sharipova)