Appollonius' circle

LocusEquation[2a==b,C] determines where to put C in order to fulfill the condition. C must take place on a circle which is called Appollonius' circle. There are many Appollonius' circles in a triangle. This one belongs to ratio 2, because b/a=2 in this case. If b/a=1, the circle is changing to a line, the bisector of AB.