Home page | Catalogue | Classes | Tables | Glossary | Notations | Links | Bibliography | Thanks | Downloads | Related Curves |
||

too complicated to be written here. Click on the link to download a text file. |
||

X(6), X(13), X(14), X(15), X(16), X(30) other points described below |
||

K909 is the locus of point M such that the directed line angles (MX13, MX14) and (MX15, MX16) or (MX13, MX15) and (MX14, MX16) are equal (mod. π). See the related property 1 in K018 and also K508. K909 is a focal cubic with focus K, invariant under the involution Psi_K described here. The orthic line (L) is the parallel at X(115) to the Euler line and the real asymptote is its homothetic under h(K, 2). The polar conic (C) of K is the circle passing through O, K, X(381). It is the image of (L) under Psi_K. The polar conic (H) of X(30) is the rectangular hyperbola passing through X(30), X(395), X(396), X(523) and the four (not always all real) centers of anallagmaty of K909. These latter points also lie on the (dashed blue) axes of the inconic with center K. These are the parallels at K to the asymptotes of the Jerabek hyperbola. K909 meets its asymptote at X, on the tangent at K to (C). P1 = X(13)X(16) /\ X(542)X, P2 = X(14)X(15) /\ X(542)X and their Psi_K images Q1, Q2 are four other points on K909. Note that X, Q1, Q2 are collinear. Hence K909 can also be seen as the locus of point M such that the directed line angles (MP1, MP2) and (MQ1, MQ2) are equal (mod. π). |