Center of the Brocard circle = Midpoint of the Circumcenter and Symmedian Point.

Center of the Brocard circle = Midpoint of the Orthocenter of the Medial Triangle and Symmedian Point.

Center of the Brocard circle = Midpoint of the Nine-Point Center of the Excentral Triangle and Symmedian Point.

Center of the Brocard circle = Midpoint of the Nine-Point Center of the Anticomplementary Triangle and Symmedian Point.

Center of the Brocard circle = Reflection of the Symmedian Point of the Medial Triangle in the Nine-Point Center of the Medial Triangle.

Center of the Brocard circle = Complement of the Orthocenter of the First Brocard Triangle.

Center of the Brocard circle = Complement of the Reflection of the Symmedian Point in the Nine-point Center.

Center of the Brocard circle = Anticomplement of the Nine-Point Center of the First Brocard Triangle.

Center of the Brocard circle = Isogonal Conjugate of the Isotomic Conjugate of the Symmedian Point of the Circum-Medial Triangle.

Center of the Brocard circle = Perspector of the Cevian Triangle of the Center of the Brocard circle and Anticevian Triangle of the Center of the Brocard circle.

Center of the Brocard circle = Perspector of the Cevian Triangle of the Center of the Brocard circle and Circumcevian Triangle of the Center of the Brocard circle.

Center of the Brocard circle = Perspector of the Cevian Triangle of the Center of the Brocard circle and Half-cevian Triangle of the Center of the Brocard circle.

Center of the Brocard circle = Perspector of the Anticevian Triangle of the Center of the Brocard circle and Circumcevian Triangle of the Center of the Brocard circle.

Center of the Brocard circle = Perspector of the Anticevian Triangle of the Center of the Brocard circle and Half-cevian Triangle of the Center of the Brocard circle.

The Center of the Brocard circle lies on the Line defined by the Centroid and Tarry Point.

The Center of the Brocard circle lies on the Brocard Axis.

The Center of the Brocard circle lies on the Line defined by the Circumcenter and First Isodynamic Point.

The Center of the Brocard circle lies on the Line defined by the Circumcenter and Second Isodynamic Point.

The Center of the Brocard circle lies on the Line defined by the Circumcenter and Brocard Midpoint.

The Center of the Brocard circle lies on the Line defined by the Circumcenter and Center of the Apollonius Circle.

The Center of the Brocard circle lies on the Line defined by the Symmedian Point and First Isodynamic Point.

The Center of the Brocard circle lies on the Line defined by the Symmedian Point and Second Isodynamic Point.

The Center of the Brocard circle lies on the Line defined by the Symmedian Point and Brocard Midpoint.

The Center of the Brocard circle lies on the Line defined by the Symmedian Point and Center of the Apollonius Circle.

The Center of the Brocard circle lies on the Line defined by the First Isodynamic Point and Second Isodynamic Point.

The Center of the Brocard circle lies on the Line defined by the First Isodynamic Point and Brocard Midpoint.

The Center of the Brocard circle lies on the Line defined by the First Isodynamic Point and Center of the Apollonius Circle.

The Center of the Brocard circle lies on the Line defined by the Second Isodynamic Point and Brocard Midpoint.

The Center of the Brocard circle lies on the Line defined by the Second Isodynamic Point and Center of the Apollonius Circle.

The Center of the Brocard circle lies on the Line defined by the Brocard Midpoint and Center of the Apollonius Circle.

The Center of the Brocard circle lies on the Brocard Circle of the First Brocard Triangle.

The Center of the Brocard circle lies on the Brocard Circle of the Second Brocard Triangle.

The Center of the Brocard circle lies on the Orthocentroidal Circle of the Medial Triangle of the First Brocard Triangle.

The Center of the Brocard circle lies on the Orthocentroidal Circle of the Medial Triangle of the Second Brocard Triangle.

The Center of the Brocard circle lies on the Bevan Circle of the Tangential Triangle of the First Brocard Triangle.

The Center of the Brocard circle lies on the Orthocentroidal Circle of the First Brocard Triangle of the Medial Triangle.

The Center of the Brocard circle lies on the Circumcircle of the First Brocard Triangle of the First Brocard Triangle.

The Center of the Brocard circle lies on the Circumcircle of the Second Brocard Triangle of the First Brocard Triangle.

The Center of the Brocard circle lies on the Circumcircle of the First Brocard Triangle of the Second Brocard Triangle.

The Center of the Brocard circle lies on the Circumcircle of the Second Brocard Triangle of the Second Brocard Triangle.