Consider a circle a and a line b interecting the circle at points I and J. There are two circles {c,d} inverting {a,b} to each other. Their centers C, D define the bisectors at I of angle AIB. The circles {c,d} are orthogonal to each other and belong to the same circle bundle generated by {a,b}. Circles {c,d} are called [Mid circles of a,b]. See MidCircles.html for the case of two intersecting circles.