X₃₆₃₉

OUTER SODDY-GERGONNE POINT

X₃₆₃₉ = X₁₆-of-intouch-triangle

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

X₃₆₃₉ (OUTER SODDY-GERGONNE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 7}, {13, 226}

• Related Centers: X₁ (INCENTER), X₇ (GERGONNE POINT), X₁₃ (1st ISOGONIC CENTER), X₂₂₆ (-CEVA CONJUGATE OF X₆₅)

Barycentrics: \((2 (2 a^{2}-(b+c) a-(b-c)^{2}) S+\sqrt{3} (-a+b+c) \cdot (2 a^{3}-(b+c) a^{2}-(b^{2}-c^{2}) \cdot (b-c))) \cdot (a-b+c) \cdot (a+b-c) : :\)

Search Value (6, 9, 13): \(-2.484266664459\)

▸ Incident Central Lines4 lines

{1, 7}, {13, 226}, {57, 1276}, {553, 559}

▸ Functional Relations2 relations

• X₃₆₃₉ = isogonal conjugate of X₃₆₇₃₈

• X₃₆₃₉ = X₁₆-of-intouch-triangle

Notes

See X₃₆₃₈ for a description of the inner and outer points.