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 |

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.