Suppose ABC is a triangle. Let U and V be the points on sideline BC met by the interior and exterior bisectors of angle A. The circle having diameter UV is called the A-Apollonian circle. The B- and C- Apollonian circles are likewise constructed.
The three circles meet in two points, labeled J and J', called the isodynamic points.
sin(A + pi/3):
sin(B + pi/3):
sin(C + pi/3)
is the first isodynamic point, and the point with trilinears
sin(A - pi/3):
sin(B - pi/3):
sin(C - pi/3)
is the second isodynamic point. Both points are discussed in
Roger A. Johnson, Advanced Euclidean Geometry, Dover Publications, Mineola, NY, 1960, pp. 294-297.
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