X₂₈₈₆

COMPLEMENTARY CONJUGATE OF X₉

X₂₈₈₆ = complement of X₅₅

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

X₂₈₈₆ (COMPLEMENTARY CONJUGATE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 11}, {5, 10}

• Related Centers: X₃₄₄₉ (1st SARAGOSSA POINT OF X₇), X₂ (CENTROID), X₁₁ (FEUERBACH POINT), X₅ (NINE-POINT CENTER), X₁₀ (SPIEKER CENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b^{3} + c^{3} - ab^{2} - ac^{2} - b^{2}c - bc^{2})\) (M. Iliev, 5/13/07)

Search Value (6, 9, 13): \(2.626318480664\)

▸ Incident Central Lines37 lines

{1, 442}, {2, 11}, {4, 958}, {5, 10}, {8, 12}, {9, 1699}, {30, 993}, {56, 377}, {63, 1836}, {75, 325}, {115, 1573}, {118, 124}, {141, 674}, {210, 908}, {214, 1484}, {226, 518}, {333, 2651}, {348, 2898}, {405, 1479}, {427, 1824}, {474, 499}, {485, 1378}, {486, 1377}, {495, 519}, {496, 1125}, {529, 956}, {982, 1086}, {1348, 1679}, {1349, 1678}, {1506, 1574}, {1676, 1681}, {1677, 1680}, {1698, 1706}, {2009, 2014}, {2010, 2013}, {2566, 2569}, {2567, 2568}

▸ Functional Relations7 relations

• X₂₈₈₆ = midpoint of X_i and X_j for these (i,j): (1, 3416), (4, 3428), (8, 2099), (63, 1836), (956, 1478)

• X₂₈₈₆ = isogonal conjugate of X₃₄₄₉

• X₂₈₈₆ = isotomic conjugate of isogonal conjugate of X₂₁₇₄₆

• X₂₈₈₆ = polar conjugate of isogonal conjugate of X₂₂₀₇₀

• X₂₈₈₆ = complement of X₅₅

• X₂₈₈₆ = complementary conjugate of X₉

• X₂₈₈₆ = crosssum of X₆ and X₂₁₇₅

Notes

X₂₈₈₆ is the center of the inellipse that is the isotomic conjugate of the isogonal conjugate of the incircle. (Randy Hutson, October 15, 2018)