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