Isodynamic point
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Every triangle in Euclidean geometry has two isodynamic points, usually denoted as S and 
. These points are the common intersection points of the three circles of Apollonius associated with the triangle; hence, the line through these points is the common radical axis for these circles. Incidentally, the centers of these circles are collinear; they all fall on the Lemoine line, which is perpendicular to the radical axis defined by the isodynamic points.
The isodynamic points have other interesting geometric properties, e.g.,
- Inversion with respect to an isodynamic point transforms the original triangle into an equilateral triangle.
- The pedal triangle of an isodynamic point is also equilateral.
[edit] See also
[edit] Reference
- Johnson RA (1960) Advanced Euclidean Geometry, Dover.
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