Figures of Gibe

Points of Gibe

First point of Gibe

  • Tracer a triangle ABC
  • Tracer the circle passing by has and B and tangent with (CB)
  • Tracer the circle passing by B and C and tangent with (CA)
  • Tracer the circle passing by C and has and tangent with (BA)
These three circles are secant in a point \ beta known as first point of Gibe of the triangle ABC (on the figure above, it is the convergent point of the three blue circles).

Second point of Gibe

  • Tracer a triangle ABC
  • Tracer the circle passing by has and B and tangent with (CA)
  • Tracer the circle passing by B and C and tangent with (BA)
  • Tracer the circle passing by C and has and tangent with (BC)
These three circles are secant in a point \ beta' known as second point of Gibe of the triangle ABC (on the figure above, it is the convergent point of the three red circles).

Angle of Gibe of the triangle

The segments uniting the points \ beta and \ beta' at the tops of the triangle constitute Isogonales particular triangle ABC. Their remarkable property is to always define the same angle \ omega, known as angle of Gibe of the triangle. \ Omega = \ widehat {\ beta AB} = \ widehat {\ beta BC} = \ widehat {\ beta CA} = \ widehat {\ beta 'CA} = \ widehat {\ beta 'BA} = \ widehat {\ beta 'BC}

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