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Circles enveloping an ellipse

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  • bbblow
    Given triangle ABC, think of family of circles homothetic to incircle at A. Choose arbitrary one of them, take intersection with line BC, and take circle which
    Message 1 of 1 , Oct 19, 2010
      Given triangle ABC, think of family of circles homothetic to incircle at A. Choose arbitrary one of them, take intersection with line BC, and take circle which has the two intersection points as the antipodal points.

      A possibly new property: such circles then envelope an ellipse, whose foci are at the tangential points of incircle and A-excircle at line BC, and passes through B and C.

      Judging by the fact that the circles do not touch the ellipse until they "grow" sufficiently large, I suspect that actually these circles might represent 2D projection of sections of a skewed ellipsoid. (Skewed as in, it will "dip in" into the page)

      Any more insights on this topic?
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