Inversion

The inversion in geometry is a cool concept and a more general concept than reflection across a plane. The figure here I drew using KIG explains what happens when inversion takes place. If there is a line outside the inverting circle its inverse becomes a circle passing through the centre. Also if there is a circle passing through the centre of the inverting circle it becomes a line. Look at how the quadrilateral behaves. So line changes to circle unless its passing through the centre in that case line remains line. Circle inverts to circle unless it is passing through the centre of the inverting circle.