Let P, Q be two isogonal points; Pa, Qa their reflections in BC; Ap the intersection between APa and BC and Aq the intersection between AQa and BC. Define analogously Bp, Bq, Cp, Cq. The six points Ap, Aq, Bp, Bq, Cp, Cq lie in a conic. When P and Q are the centroid G and the symmedian K, the center of the conic is collinear with G and K and the conic goes through the point X(125).