The figure determined by four lines, no three of which are concurrent, and their six points of intersection. Note that this figure is different from a complete quadrangle. A complete quadrilateral has three diagonals (compared to two for an ordinary quadrilateral). The midpoints of the diagonals of a complete quadrilateral are collinear on a line M. A theorem due to Steiner (Mention 1862ab, Johnson 1929, Steiner 1971) states that in a complete quadrilateral, the bisectors of angles are concurrent at 16 points which are the incenters and excenters of the four triangles. Furthermore, these points are the intersections of two sets of four circles each of which is a member of a conjugate coaxal system. The axes of these systems intersect at the point common to the circumcircles of the quadrilateral.
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Jonathan is doing really well in all of his classes this semester, 5 A’s & 2 B’s (he has a computer essentials class instead of PLC). In his Algebra class that Nathan is helping him with he has an A+.
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