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(2), X(3), X(6), X(68), X(394), X(577), X(1147), X(6503), X(60775)

isogonal conjugate of X(60783), X(2)-Ceva conjugate of X(68)

vertices A', B', C' of the medial triangle

vertices Pa, Pb, Pc of the anticevian triangle of O

infinite points of pK(X6, X6515)

points Q1, Q2, Q3 of K1421 = pK(X6, X394) on (O), see below

Geometric properties :

K1420 is the isogonal transform of K621 = pK(X393, X2052) and the complement of pK(X2, X317).

K1420 meets the symmedians again at the vertices of a triangle TaTbTc perspective to the medial triangle at X(6503) and to the anticevian triangle of O at X(1147). Note that these two latter triangles are perspective at X(6).

***

The orthocenter of Q1Q2Q3 is X(394). Its vertices lie on a pencil of rectangular hyperbolas obviously passing through X(394). Here are some of the most remarkable examples with the fourth point P on (O) :

• P = X(99) : {X(2), X(99), X(394), X(801), X(6503), X(3413), X(3414)}, homothetic to the Kiepert hyperbola

• P = X(110) : {X(6), X(110), X(394), X(1147), X(1498), X(1660), X(2574), X(2575)}, homothetic to the Jerabek hyperbola

• P = X(476) : {X(22), X(30), X(230), X(394), X(476), X(523)}

• P = X(805) : {X(394), X(511), X(512), X(805), X(3231)}

The inconic with perspector X(801) is inscribed in Q1Q2Q3.

K1420 meets the sidelines of Q1Q2Q3 again at three points which lie on the bicevian conic C(X2, X394).