The excentral-hexyl ellipse is the ellipse passing through vertices of the excentral and hexyl triangles. It has center at the circumcenter O. It has trilinear equation a(a + b - c)(a - b + c)(b + c) α^2 + 2a b c(a + b + c) βα + 2a b c(a + b + c) γα - b(a - b - c)(a + b - c)(a + c) β^2 - (a + b)(a - b - c) c(a - b + c) γ^2 + 2a b c(a + b + c) βγ.

Bevan circle | circumellipse | excentral triangle | hexyl triangle