When a circle is excised from a bigger circle so that the center of mass of the remaining portion is at a point in the inner edge, then the radii of the two circles are in the golden ratio. The same is true for any even sided regular polygon for excissions along certain symmetry axes of the figure as presented in Pathak and Singh (2016 Eur. J. Phys. 37 055001). We extend the result to shapes that do not have any rotational symmetry and also along axes which are not symmetry axes.