X₁₁₆₃

INNER GREBE-ORTHIC PERSPECTOR

X₁₁₆₃ = X₄-Ceva conjugate of X₃₁₂₈

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₁₆₃ (INNER GREBE-ORTHIC PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 1161}, {428, 1162}

• Related Centers: X₄ (ORTHOCENTER), X₃₁₂₈ (-CEVA CONJUGATE OF X₁₁₆₃), X₁₁₆₁ (CIRCUMCENTER OF INNER GREBE TRIANGLE), X₄₂₈ (EULER X₃₈-5th-SUBSTITUTION POINT), X₁₁₆₂ (OUTER GREBE-ORTHIC PERSPECTOR)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (\operatorname{area} - a^{2})(2 \operatorname{area} - b^{2} - c^{2})/[a(b^{2} + c^{2} - a^{2})]\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(-0.836712920829\)

▸ Incident Central Lines2 lines

{4, 1161}, {428, 1162}

▸ Functional Relations1 relation

• X₁₁₆₃ = X₄-Ceva conjugate of X₃₁₂₈

Notes

See Hyacinthos #6537.