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(3), X(5), X(30), X(265), X(1807), X(7100), X(10217), X(10218), X(15392), X(20123)

X(50461) → X(50469)

cevians of X(265)

other points below

Geometric properties :

The vertices of the orthocentroidal triangle are the orthogonal projections of G on the altitudes of ABC. They lie on K005, K295, K397.

Their isogonal conjugates are the vertices of the orthocentroidal-isogonic triangle T. These points lie on the cevian lines of O and on K005, K297, K397.

The locus of P whose cevian triangle is perspective to this triangle T is K1278 = pK(X3 x X265, X265), and the perspector lies on K005. The barycentric product X3 x X265 is now X(50433) in ETC.

Note that the locus of P whose anticevian triangle is perspective to T is K001, and the perspector also lies on K005.

The locus of P whose antipedal triangle is perspective to T is K1279 = pK(X6, aX1514), where aX1514 is the anticomplement X(50434) of X(1514).

Properties :

• K1278 meets the circumcircle at the same points as pK(X6, X3153).

• K1278 meets the line at infinity at the same points as pK(X6, S), where S is the intersection of the lines {4,52}, {30,74) and many others. The two cubics meet at six finite points on the Kiepert hyperbola. S is now X(50435) in ETC.

• the polar conic of O is the Jerabek hyperbola (J), hence the tangents of K1278 at A, B, C, X(265) concur at O, the isopivot.

• K1278 is the barycentric product X(265) x K856.