Spieker circle

  Triangle ABC and its medial triangle
  Spieker circle of ABC (incircle of the medial triangle; centered at the Spieker center X10)
  Cleavers of the triangle (concurrent at the Spieker center)

In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker.[1] Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the center of mass of the uniform-density boundary of triangle.[1] The Spieker center is also the point where all three cleavers of the triangle (perimeter bisectors with an endpoint at a side's midpoint) intersect each other.[1]

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