The midpoint of the first and second Brocard points Ω and Ω'. It has equivalent triangle center functions α | = | a(b^2 + c^2) α | = | sin(A + ω), where ω is the Brocard angle. It is Kimberling center X_39. The Brocard midpoint lies on the Brocard axis and is the center of the Gallatly, half-Moses, and Moses circles.

Brocard points | first Brocard point | second Brocard point