The Brocard axis is the line 
passing through the symmedian
point 
and circumcenter 
of a triangle, where the segment
is the Brocard
diameter (Kimberling 1998, p. 150). The Brocard axis is perpendicular
to the Lemoine axis and is the isogonal
conjugate of the Kiepert hyperbola.
It is central line 
and has equivalent trilinear equations
 |
and
 |
It passes through Kimberling centers 
for 
(circumcenter 
), 6 (symmedian point 
), 15 (first
isodynamic point 
),
16 (second isodynamic point 
), 32 (third power point),
39 (Brocard midpoint), 50, 52, 58, 61, 62, 182,
187, 216, 284, 371 (Kenmotu point), 372, 386, 389
(Taylor center), 500, 511, 566, 567, 568, 569, 570,
571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 800, 970, 991,
1030, 1151, 1152, 1160, 1161, 1182, 1192, 1207, 1326, 1333, 1340, 1341, 1342, 1343,
1350, 1351, 1379, 1380, 1384, 1504, 1505, 1570, 1578, 1579, 1609, 1620, 1662, 1663,
1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1683, 1684, 1685, 1686, 1687, 1688,
1689, 1690, 1691, 1692, 1693, 1694, 1805, 1806, 1970, 1983, 2011, 2012, 2019, 2020,
2021, 2022, 2024, 2025, 2026, 2027, 2028, 2029, 2030, 2031, 2032, 2033, 2034, 2035,
2036, 2037, 2038, 2055, 2076, 2080, 2088, 2092, 2193, 2220, 2245, 2271, 2278, 2305,
2420, 2456, 2458, 2459, 2460, 2461, 2462, 2558, 2559, 2560, 2561, 2562, 2563, 2673,
2674, 2965, 3001, 3002, 3003, and 3053.
Note that the Brocard axis is not equivalent to the Brocard line.
