Coxeter-Theorem 8.31

8.31. SEYDEWITZ'S THEOREM: If a triangle is inscribed in a conic, any line conjugate to one side meets the other two sides in conjugate points. As in Figure 8.2 A (Left), construct an inscribed triangle PQR. Any line c conjugate to PQ is the polar of some point C on PQ. Let RC meet the conic again in S. Since the diagonal triangle of a quadrangle inscribed in a conic is self polar (by 8.21), the diagonal points of the quadrangle PQRS form a self-polar triangle ABC whose side c contains the conjugate points A and B: one on QR and the other on RP.