The three tangents at the vertices of a triangle inscribed in a conic meet the opposite sides in three points on a straight line.
Fig. 18
78. Degenerate conic. If we apply Pascal's theorem to a degenerate conic made up of a pair of straight lines, we get the following theorem (Fig. 18):
If three points, A, B, C, are chosen on one line, and three points, A', B', C', are chosen on another, then the three points L = AB'-A'B, M = BC'-B'C, N = CA'-C'A are all on a straight line.
PROBLEMS
1. In Fig. 12, select different lines u and trace the locus of the center of perspectivity M of the lines u and u'.
2. Given four points, A, B, C, D, in the plane, construct a fifth point P such that the lines PA, PB, PC, PD shall be four harmonic lines.