The Johnson circles are a triplet of congruent circles sharing a single point. Every triangle has exactly two Johnson triplets. Properties: • The locators are the centers of the three circles. They form the Johnson triangle with circumcircle of the same radius. • Johnson's theorem: the "reference triangle" with vertices the points of two-fold intersection has, surprisingly, a circumcircle of the same radius. • The reference triangle is congruent to the Johnson triangle by homothety of factor ... . • The anticomplementary circle with twice the radius touches the Johnson circles. • The inscribed anticomplementary triangle is homothetic to the Johnson triangle with factor 2. • The three locators and the origin are, surprisingly, such that each is the orthocenter of the three others. • The homothetic center of the Johnson and reference triangle is the center of the nine-point circle of the reference triangle.


    Education Levels:


      EUN,LOM,LRE4,work-cmr-id:398935,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/TheJohnsonCircles/,ilox,learning resource exchange,LRE metadata application profile,LRE


      Access Privileges:

      Public - Available to anyone

      License Deed:

      Creative Commons Attribution 3.0


      This resource has not yet been aligned.
      Curriki Rating
      'NR' - This resource has not been rated
      'NR' - This resource has not been rated

      This resource has not yet been reviewed.

      Not Rated Yet.

      Non-profit Tax ID # 203478467