X₁₈₉₉

ZOSMA TRANSFORM OF X₁₀₉₆

X₁₈₉₉ = reflection of X₃₉₄ in X₁₃₆₈

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

X₁₈₉₉ (ZOSMA TRANSFORM OF X₁₀₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {394, 1368}

• Related Centers: X₃₉₄ (-CEVA CONJUGATE OF X₃), X₁₃₆₈ (COMPLEMENTARY CONJUGATE OF X₆)

Trilinears: \((y + z) \sec A : :\), where \(x : y : z\) = X₁₀₉₆

Barycentrics: \((-a^{2}+b^{2}+c^{2}) (a^{4}+b^{4}-2 b^{2} c^{2}+c^{4}) : :\)

Search Value (6, 9, 13): \(4.553749431107\)

▸ Alternate Coordinates1 form

• Trilinears: \(2 b c - a b \sec B - a c \sec C : :\)

▸ Incident Central Lines63 lines

{2, 98}, {3, 68}, {4, 51}, {5, 1181}, {6, 66}, {20, 1204}, {22, 3580}, {25, 1503}, {54, 70}, {64, 1885}, {65, 5130}, {67, 5486}, {69, 305}, {154, 468}, {217, 2548}, {235, 1498}, {265, 974}, {315, 3978}, {388, 1425}, {394, 1368}, {407, 5786}, {429, 5706}, {442, 5810}, {462, 5869}, {463, 5868}, {497, 3270}, {511, 1370}, {578, 3541}, {686, 804}, {858, 1993}, {860, 5767}, {940, 5820}, {1092, 3546}, {1147, 3548}, {1321, 3070}, {1322, 3071}, {1495, 6353}, {1587, 3127}, {1588, 3128}, {1591, 6289}, {1592, 6290}, {1593, 6247}, {1824, 5928}, {1864, 5101}, {1974, 5596}, {2072, 5654}, {2450, 3767}, {2549, 3269}, {2550, 3611}, {2888, 3523}, {2892, 5095}, {2992, 2993}, {3134, 5877}, {3136, 5816}, {3142, 5713}, {3332, 4207}, {3549, 5449}, {3818, 5943}, {3851, 5644}, {3926, 4121}, {5064, 5480}, {5133, 5422}, {5200, 5870}

▸ Functional Relations8 relations

• X₁₈₉₉ = reflection of X₃₉₄ in X₁₃₆₈

• X₁₈₉₉ = isotomic conjugate of X₃₄₄₀₅

• X₁₈₉₉ = crosspoint of X₄ and X₆₉

• X₁₈₉₉ = crosssum of X_i and X_j for these (i,j): (3, 25), (52, 418), (206, 571)

• X₁₈₉₉ = anticomplement of X₉₃₀₆

• X₁₈₉₉ = crossdifference of every pair of points on line X₃₅₆₉X₆₇₅₃

• X₁₈₉₉ = X₁₃₇₀-of-1st-Brocard-triangle

• X₁₈₉₉ = X₂₀₀-of-orthic-triangle if ABC is acute