Isodynamic point

The two isodynamic points belong to the excellent points of a triangle.

Given a triangle ABC with the bisector of its interior and exterior angles. U1 is the intersection of the angle bisector of the straight line BC, V1 of the point of intersection of the corresponding Außenwinkelhalbierenden with BC. Accordingly, the points U2 and V2 (each on CA ) and U3 and V3 are ( respectively on AB) defined. Then, the three circles with the diameters of [U1 V1 ], [ U2 V2 ] and [ U3 V3 ] two points S and S ' together. S is called the first isodynamischer point ( Kimberling number), S ' as 2nd isodynamischer point ( Kimberling number).

Coordinates

Properties

  • The two points are isogonal conjugated isodynamic to the two Fermat points.
  • The inversion ( mirroring circle ) at the periphery leads one of the two points above isodynamic in the other.
  • The Fußpunktdreiecke the two isodynamic points are equal to each other.
  • The isodynamic points lie on the Brocard axis.
  • The three circles are circles of Apollonius
Triangle center Trilinear coordinates Wolfram Research
419420
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