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X(3), X(30), X(36), X(186) Na, Nb, Nc : vertices of the circumnormal triangle inverses of the excenters in the circumcircle 

The locus of point P such that the circumcevian and reflection triangles of P are perspective is the McCay cubic. The locus of the perspector is Q047, the McCay quintic. Q047 is the inversive image of the McCay cubic in the circumcircle. It is a bicircular quintic with a real asymptote parallel at X(74) to the Euler line. O is a triple point on the curve with tangents the altitudes of the circumnormal triangle. K038 is the locus of points whose polar conic in Q047 is a rectangular hyperbola. In other words, the cubic is the Laplacian of the quintic. 
