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There is a well-known model of 2-dimensional projective geometry points and lines including points at infinity and line at infinity in terms of three dimensional Euclidean geometry, namely, ordinary projective points represented by Euclidean straight lines through the origin and intersecting the Euclidean plane z = 1; ordinary projective lines by Euclidean planes through the origin intersecting the Euclidean plane z= 1; and the projective points at infinity by Euclidean straight lines through the origin but lying on the Euclidean plane z = 0; and the line at infinity by the Euclidean plane z = 0, itself. This model also shows that parallel projective lines on the Euclidean z = 1, do meet in a point at infinity, namely, the Euclidean line of intersection of the two Euclidean planes representing the two parallel projective lines. Is there a similarly explicit representational model that shows that any two circles in the complex projective plane intersecting at two fixed imaginary points?

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