X₃₅₅₅

DOSA POINT

X₃₅₅₅ = anticomplement of X₃₄₇₉₀

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

X₃₅₅₅ (DOSA POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {20, 145}

• Related Centers: X₁ (INCENTER), X₆ (SYMMEDIAN POINT), X₂₀ (DE LONGCHAMPS POINT), X₁₄₅ (ANTICOMPLEMENT OF NAGEL POINT)

Trilinears: \(bc(2a - b \cos A - c \cos A) : :\)

Search Value (6, 9, 13): \(-2.287454535590\)

▸ Incident Central Lines29 lines

{1, 6}, {8, 443}, {10, 354}, {20, 145}, {28, 1280}, {63, 3295}, {65, 519}, {78, 999}, {200, 474}, {210, 1125}, {244, 3214}, {319, 2891}, {329, 1058}, {379, 3187}, {388, 3419}, {496, 908}, {528, 1770}, {758, 3057}, {912, 1482}, {938, 3421}, {962, 971}, {997, 3304}, {1009, 2350}, {1320, 2771}, {1376, 3338}, {1858, 2098}, {1872, 1897}, {1998, 3149}, {2093, 2136}

▸ Functional Relations4 relations

• X₃₅₅₅ = reflection of X_i in X_j for these (i,j): (8, 942), (72, 1), (3057, 3244)

• X₃₅₅₅ = anticomplement of X₃₄₇₉₀

• X₃₅₅₅ = X₁₆₆₅₅-of-excentral-triangle

• X₃₅₅₅ = orthologic center of these triangles: Hutson-extouch to Hutson-intouch; the reciprocal orthologic center is X₅₉₂₀

Notes

See Tibor Dosa, “Some triangle centers associated with excircles,” :cite:`Forum Geometricorum <forum-geometricorum>` 7 151-158.