The Fourth Intersection Point of the Circumconic
Construct a circumconic with center P. Let A', B', and C' be the antipodal points of A, B, and C. Circles AB'C', BA'C' and CA'B'
intersect at the fourth intersection point T of the circumconic and the circumcircle. Circles ABC', ACB', and BCA' intersect at the
antipodal point T'