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K889

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

X(2), X(100), X(187), X(353), X(739), X(1083), X(1340), X(1341), X(5638), X(5639), X(11650), X(11651), X(11652)

other points below

K889 is a circular cubic invariant under the involution Psi described in the page K018 and in the paper "Orthocorrespondence and Orthopivotal Cubics", §5. See also the analogous focal cubic K508. K889 is a Psi-cubic as in Table 60.

K889 is an isogonal pK with pivot S (a complicated point at infinity, SEARCH = -7.45403759640433) in the triangle X(2)X(187)X(353) and it must contain the in/excenters of this triangle which are X(1340), X(1341), X(5638), X(5639).

Other points on K889 :

• E = Psi(X739), SEARCH = 0.856355341120740, on the Brocard circle.

• P and Q on the circumcircle :

P = X(100)X(5638) /\ X(739)X(5639) /\ X(1340)E /\ X(1341)X(1083), SEARCH = -0.596949864780888,

Q = X(100)X(5639) /\ X(739)X(5638) /\ X(1341)E /\ X(1340)X(1083), SEARCH = 8.64895132333979.

E = X(11650), P = X(11651), Q = X(11652) in ETC now (2017-01-10)

Note that X(6), P, Q are collinear. Psi(P) and Psi(Q) are the last common points of K889 and the Brocard circle.

The singular focus F is very complicated with SEARCH = 1.55523147653427.