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(42), X(213), X(238), X(741), X(1914), X(2054), X(3747)

vertices of the cevian triangle of X(6)

points on (O) and on the Lemoine axis

other points below

Geometric properties :

The cevian triangle of P is perspective to the circumcevian triangle of X(3747) if and only if P lies on K1417.

Other points on K1417

P1 = a^2 (b+c)^2 (a^2-b c)^2 : : , SEARCH = 1.46042736107142, on the Brocard ellipse.

P2 = a^2 (a^2-b c) (a^2+a b-b^2+a c-b c-c^2) : : , SEARCH = 1.05866169465305.

P3 = a^2 (b+c) (a^2-b c) (a^2+3 a b+b^2+a c+b c-c^2) (a^2+a b-b^2+3 a c+b c+c^2) (a^4+2 a^3 b+a^2 b^2-2 a b^3-b^4+2 a^3 c+4 a^2 b c-2 b^3 c+a^2 c^2-b^2 c^2-2 a c^3-2 b c^3-c^4) : : , SEARCH = 0.713331856132708.

P4 = a^2 (a b^2+a^2 c+2 a b c+b^2 c+a c^2) (a^2 b+a b^2+2 a b c+a c^2+b c^2) (a^2 b^2+3 a^2 b c+a b^2 c+a^2 c^2+a b c^2-b^2 c^2) : : , SEARCH = 0.478678164642443.

P5 = a (a^2-b c) (a^2 b^2+a^2 b c-a b^2 c+a^2 c^2-a b c^2-b^2 c^2) : : , SEARCH = 1.97305014393442.

P6 = a^2 (a^2-a b-b^2-a c-3 b c-c^2) (a b^2+a^2 c+2 a b c+b^2 c+a c^2) (a^2 b+a b^2+2 a b c+a c^2+b c^2) : : , SEARCH = 1.60845838640972.