X₁₃₇₆

EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE)

X₁₃₇₆ is the exsimilicenter(circumcircle, Spieker circle).

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

X₁₃₇₆ (EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 11}, {3, 10}

• Related Centers: X₂ (CENTROID), X₁₁ (FEUERBACH POINT), X₃ (CIRCUMCENTER), X₁₀ (SPIEKER CENTER)

Trilinears: \(a^{2} - ab - ac + 2bc : :\)

Barycentrics: \(b + c - a \cos A : :\)

Search Value (6, 9, 13): \(2.625141511472\)

▸ Linear Combinations1 combination

• X₁₃₇₆ = X₁ - \(3\) X₂ + \((r/R)\) X₃ = \(r\) X₃ - \(2R\) X₁₀ = \(R\) X₁ - \(r\) X₃ + \(R\) X₈

▸ Incident Central Lines32 lines

{1, 474}, {2, 11}, {3, 10}, {4, 1329}, {6, 43}, {7, 480}, {8, 56}, {9, 165}, {12, 377}, {31, 899}, {35, 405}, {36, 956}, {40, 936}, {42, 750}, {45, 846}, {46, 72}, {57, 200}, {63, 210}, {65, 78}, {71, 965}, {75, 183}, {226, 1260}, {227, 1038}, {371, 1377}, {372, 1378}, {442, 498}, {517, 997}, {519, 999}, {748, 902}, {851, 1211}, {978, 1191}, {982, 1054}

▸ Functional Relations11 relations

• X₁₃₇₆ = midpoint of X_i and X_j for these (i,j): (8, 3476), (57, 200), (329, 3474)

• X₁₃₇₆ = isogonal conjugate of X₉₃₀₉

• X₁₃₇₆ = homothetic center of inner-Conway triangle and cross-triangle of Ursa-major and Ursa-minor triangles

• X₁₃₇₆ = complement of X₄₉₇

• X₁₃₇₆ = X₂₉₄-Ceva conjugate of X₅₁₈

• X₁₃₇₆ = cevapoint of X₄₃ and X₁₆₅

• X₁₃₇₆ = anticomplement of X₃₈₁₆

• X₁₃₇₆ = crosssum of PU(46)

• X₁₃₇₆ = crosspoint of PU(112)

• X₁₃₇₆ = crossdifference of every pair of points on line X₆₆₅X₄₀₈₃

• X₁₃₇₆ = homothetic center of ABC and cross-triangle of ABC and inner Johnson triangle