Let P be a point in the circumcircle. The perpendicular from P to BC cuts AB at Ab and AC at Ac. Define analogously Bc, Ba, Ca, Cb. The lines AcBc, BaCa, CbAb bound a triangle A'B'C' and the six points A, B, C, A', B', C' lie in a conic. The perspector of this conic belongs to the circumconic with perspector X(184).