X₁₁₆₂

OUTER GREBE-ORTHIC PERSPECTOR

X₁₁₆₂ = X₄-Ceva conjugate of X₃₁₂₇

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

X₁₁₆₂ (OUTER GREBE-ORTHIC PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 1160}, {428, 1163}

• Related Centers: X₄ (ORTHOCENTER), X₃₁₂₇ (-CEVA CONJUGATE OF X₁₁₆₂), X₁₁₆₀ (CIRCUMCENTER OF OUTER GREBE TRIANGLE), X₄₂₈ (EULER X₃₈-5th-SUBSTITUTION POINT), X₁₁₆₃ (INNER GREBE-ORTHIC PERSPECTOR)

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

Search Value (6, 9, 13): \(-2.089318682845\)

▸ Incident Central Lines2 lines

{4, 1160}, {428, 1163}

▸ Functional Relations1 relation

• X₁₁₆₂ = X₄-Ceva conjugate of X₃₁₂₇

Notes

See Hyacinthos #6537.