Bisector via angles (isosceles triangle)

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


  • 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 LocusEquation[α==β,C], but this kind of easier input syntax (as of July 2016) is not yet supported.