表明旅行商（TSP）的2倍最优近似算法不能计算出最优解

I have a review for the final exam and this question has been particularly confusing for me. I need an example on 3 vertices that the 2 times optimal approximation algorithm for traveling salesman problem (TSP) does not compute a 2 times optimal solution, if the triangular inequality does not hold for the cost. I tried an example with a triangle with costs of sides 1, 1, and 10. However, to get the Hamiltonian cycle, all three sides have to be traversed anyways. Then the optimal solution would be no different than the approximation solution with this algorithm. Am I looking at this all wrong? I would appreciate any help on this.I have a review for the final exam and this que