In this paper, we study the problem of bi-objective path planning with the objectives minimizing the length and maximizing the clearance of the path, that is, maximizing the minimum distance between the path and the obstacles. The goal is to find Pareto optimal paths. We consider the case that the first objective is measured using the Manhattan metric and the second one using the Euclidean metric, and propose an $$O(n^3 \log n)$$ time algorithm, where n is the total number of vertices of the obstacles. Also, we state that the algorithm results in a ($$\sqrt{2}, 1$$)-approximation solution when both the objectives are measured using the Euclidean metric.