Spieker circle

As Spieker point or spike - center of a triangle is called the incenter of the triangle associated center. One finds the spike point thus characterized in that connecting the centers of the sides of the given triangle together, and the bisector of this brings the center of the triangle section. The Spieker point is named after the high school teacher Theodor Spieker ( 1823-1913 ).

Properties

  • The Spieker point of a triangle coincides with the center of gravity of the corresponding triangle scope, ie So, for example, the focus of a wire model of the triangle.
  • The Spieker point is the incenter, the center of gravity and the nail - point on a straight line. It bisects the link between the incenter and the nail point.
  • The Spieker point is the center of orthocenter and Bevan point.
  • The Spieker point is the center of a circle that intersects the three excircles right angles.
  • The Spieker point lies on the Kiepert hyperbola.

Coordinates

  • Eric W. Weisstein: Spieker Center. In: MathWorld (English).
  • Spieker point - a visualization with GeoGebra, Spieker point, inscribed circle and focus lie on a straight
  • Spieker point and excircles - a visualization with GeoGebra, the Spieker point is the center of a circle orthogonal (perpendicular ) cuts the excircles of the triangle.
Nagel point Trilinear coordinates Wolfram Research
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