The third Brocard point has triangle center function α = a^(-3) and is Kimberling center X_76. The point may have received its name since its barycentric coordinates are (a^(-2), b^(-2), c^(-2)), thus completing the cyclic permutation of barycentric coordinates for the first Brocard point, namely (b^(-2), a^(-2), c^(-2)), and the second Brocard point, namely (c^(-2), a^(-2), b^(-2)).

Brocard points | first Brocard point | second Brocard point

Pierre René Jean Baptiste Henri Brocard