The first and second isodynamic points of a triangle Δ A B C can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of bisectors intersects a side of the triangle (or its extension) in two points D_(i1) and D_(i2), for i = 1, 2, 3. The three circles having D_11 D_12, D_21 D_22, and D_31 D_32 as diameters are the Apollonius circles C_1, C_2, and C_3. The points S and S' in which the three Apollonius circles intersect are the first and second isodynamic points, respectively. The two isodynamic points of a reference triangle Δ A B C are mutually inverse with respect to the circumcircle of Δ A B C.

Apollonius circle | Brocard axis | Fermat points | first isodynamic point | Parry circle | second isodynamic point | triangle centroid