Let P, P* be two isogonal points and A', B', C', A", B", C" their orthogonal projections on the sides. Let Xa be the orthocenter of A'B"C", Ya the orthocenter of A"B'C', and define analogously Xb, Yb, Xc, Yc. The six points Xa, Ya, Xb, Yb, Xc, Yc lie in a rectangular hyperbola and are opposite in it.