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(4), X(5), X(32), X(39), X(52), X(211), X(217), X(2909), X(3199), X(15897), X(27366), X(27367), X(27369), X(27370), X(27371), X(27372), X(27373), X(27374), X(27375), X(27376), X(27377)

vertices of the orthic triangle

other points below

Geometric properties :

K1088 is the isogonal pK with pivot the barycentric product P = X(27374) = X(5) x X(3051) with respect to the orthic triangle. It is the locus of M such that P, M and the isogonal conjugate M* of M with respect to the orthic triangle are collinear. K1088 is then a member of the Euler orthic pencil. Recall that M* is also the X(4)-Ceva conjugate of M.

(S) is the circum-conic with perspector P. It meets K1088 at S1, S2, S3 such that the orthic inconic (C) is inscribed in the triangle S1S32S3.

The contacts R1, R2, R3 of (C) with the triangle S1S32S3 also lie on K1088.

E = X(27369) = a^4 (b^2 + c^2) / SA : : is the third point of K1088 on the Euler line.

Q1, Q2, Q3 lie on K1088, the circumcircle and pK(X6, Q) where

Q = a^8 b^2-2 a^6 b^4+a^4 b^6+a^8 c^2-6 a^6 b^2 c^2-2 a^4 b^4 c^2+2 a^2 b^6 c^2-b^8 c^2-2 a^6 c^4-2 a^4 b^2 c^4+2 a^2 b^4 c^4+b^6 c^4+a^4 c^6+2 a^2 b^2 c^6+b^4 c^6-b^2 c^8 : : , SEARCH = -1.75902363004983.

K1089 is the SS{a → √a} image of K1088. Note that the SS{a → √a} image of (C) is the incircle of ABC.