[code]LocusEquation[AreCongruent[α,β],C][/code] determines where to put [i]C[/i] in order to the angles [i]α[/i] and [i]β[/i] are equal. With no doubt [i]C[/i] must take place on the bisector of [i]AB[/i]. In such cases the triangle will be isosceles.[br][br]There is, however, one remarkable issue. GeoGebra draws not only the bisector of [i]AB[/i], but also [i]AB[/i], as the final result. The reason is that instead of computing [i]α[/i]=[i]β[/i], cos([i]α[/i])=cos([i]β[/i]) is used. This problem has its roots in complex algebraic geometry, and currently cannot be handled elegantly in GeoGebra.

[list][*]This is a "heavy" applet. Currently (as of July 2016) it requires too much resources to run in the web version of GeoGebra. You may encounter problems when dragging the points.[/*][*]The same effect should be performed by entering [code]LocusEquation[α==β,C][/code], but this kind of easier input syntax (as of July 2016) is not yet supported.[br][/*][/list]