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X(178) 2nd mid-arc point

2nd mid-arc point

The 2nd mid-arc point is constructed as follows:
  • Construct the incircle of triangle ABC.
  • Construct A',B',C' as the first points of intersection of the angle bisectors of ABC with its incircle.
  • Define A",B",C" as the midpoints of segments a, b, and c, respectively.
  • The lines A'A",B'B",C'C" concur in P, triangle center X(178).
The barycentric coordinates of this point depend on the arcs of the triangle.

2de boogmidden punt

Het 2de boogmidden punt construeer je als volgt:
  • Construeer de ingeschreven cirkel van ABC.
  • Constructeer A',B',C' als de eerste snijpunten van de bissectrices van ABC en de ingeschreven cirkel.
  • Definieer A",B",C" als de middens van de zijden a, b en c.
  • De rechten A'A",B'B",C'C" snijden elkar in P, driehoekscentrum X(178).