fourth Brocard triangle

Let the circles c_2 and c_3^, used in the construction of the Brocard points which are tangent to A_2 A_3 at A_2 and A_3, respectively, meet again at D_A. The points D_A D_B D_C then define the D-triangle, also known as the fourth Brocard triangle (Gibert). It has trilinear vertex matrix [a sec A | 2c | 2b 2c | b sec B | 2a 2b | 2a | c sec C].

Apollonius circle | Brocard points | second Brocard triangle | third Brocard triangle