X₁₈₃₇

ZOSMA TRANSFORM OF X₃₄

X₁₈₃₇ = inverse-in-Fuhrmann-circle of X₁₁

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

X₁₈₃₇ (ZOSMA TRANSFORM OF X₃₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {65, 1898}

• Related Centers: X₆₅ (ORTHOCENTER OF THE INTOUCH TRIANGLE), X₁₈₉₈ (ZOSMA TRANSFORM OF X₁₀₆₈)

Trilinears: \((y + z) \sec A : (z + x) \sec B : (x + y) \sec C\), where \(x : y : z\) = X₃₄

Barycentrics: \((y + z) \tan A : (z + x) \tan B : (x + y) \tan C\), where \(x : y : z\) = X₃₄

Search Value (6, 9, 13): \(2.361857892673\)

▸ Alternate Coordinates1 form

• Trilinears: \(\cos B + \cos C - 2 \cos B \cos C : :\)

▸ Incident Central Lines24 lines

{1, 5}, {3, 1737}, {4, 65}, {6, 1826}, {8, 210}, {10, 55}, {19, 1852}, {20, 1155}, {30, 46}, {33, 429}, {40, 1728}, {56, 515}, {78, 1329}, {221, 1877}, {354, 388}, {382, 1770}, {499, 1385}, {517, 1479}, {942, 1478}, {944, 1319}, {1040, 1722}, {1399, 1771}, {1464, 1745}, {1853, 1854}

▸ Functional Relations11 relations

• X₁₈₃₇ = midpoint of X₆₅ and X₁₈₉₈

• X₁₈₃₇ = reflection of X_i in X_j for these (i,j): (1, 496), (56, 1210), (78, 1329)

• X₁₈₃₇ = isotomic conjugate of X₃₄₃₉₉

• X₁₈₃₇ = inverse-in-Fuhrmann-circle of X₁₁

• X₁₈₃₇ = crosspoint of X₄ and X₈

• X₁₈₃₇ = crosssum of X₃ and X₅₆

• X₁₈₃₇ = X₂₄-of-Fuhrmann-triangle

• X₁₈₃₇ = inverse-in-Feuerbach-hyperbola of X₃₅₅

• X₁₈₃₇ = {X₁,X₈₀}-harmonic conjugate of X₃₅₅

• X₁₈₃₇ = {X₄,X₆₅}-harmonic conjugate of X₁₈₃₆

• X₁₈₃₇ = Ursa-major-to-Ursa-minor similarity image of X₁