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This paper presents a method for obstacle avoidance and path-finding amid circular objects. The input data are circles and the output is a sequence of circles. The output circles represent a possible path, to a target, for a holonomic mobile robot. The method uses a solution to the Apollonius Tangency problem to find the maximum spanning circles amid the input circles. The radii of the circles can be set by desired clearance to nearby obstacles, from sensor parameters, or model parameters from extracted features. The method is intuitive and rather easily implemented and suits well for mobile robots, especially mobile robots with circular shape. It can be implemented with a depth-first approach where the target bearing angle is used as criteria in a divide and conquer step. The method was tested on sensor data registered by a laser range finder.