Hexagon circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. If the successive sides of a cyclic hexagon are "a", "b", "c", "d", "e", "f", then the three main diagonals intersect in a single point if and only if . If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent. If a hexagon has vertices
Real projective plane of the (equivalent) ordinary disk are identified with each other; this is how a real projective plane is formed out of a disk. Therefore the surface shown in Figure 1 (cross-cap with disk) is topologically equivalent to the real projective plane "RP". The points in the plane can be represented by homogeneous coordinates. A point has homogeneous coordinates ["x" : "y" : "z"], where the coordinates ["x" : "y" : "z"] and ["tx" : "ty" : "tz"] are considered to represent the same point, for all nonzero values of "t". The points with coordinates ["x" : "y" : 1] are