X₁₈₆₁

ZOSMA TRANSFORM OF X₂₃₈

The trilinear polar of X₁₈₆₁ passes through X₄₀₈₈.

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

X₁₈₆₁ (ZOSMA TRANSFORM OF X₂₃₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 9}, {2, 33}

• Related Centers: X₄ (ORTHOCENTER), X₉ (MITTENPUNKT), X₂ (CENTROID), X₃₃ (PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES)

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X₂₃₈

Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X₂₃₈

Search Value (6, 9, 13): \(1.870280861341\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines27 lines

{1, 475}, {2, 33}, {4, 9}, {5, 1872}, {8, 34}, {12, 1887}, {25, 1376}, {75, 225}, {208, 1788}, {232, 1575}, {235, 1329}, {240, 522}, {378, 993}, {406, 1698}, {427, 1824}, {429, 1900}, {468, 1862}, {518, 1876}, {519, 1870}, {594, 1841}, {765, 1877}, {908, 1830}, {958, 1593}, {960, 1902}, {1528, 1532}, {1595, 1871}, {1829, 1883}

▸ Functional Relations10 relations

• X₁₈₆₁ = isogonal conjugate of X₃₆₀₅₇

• X₁₈₆₁ = isotomic conjugate of X₃₁₆₃₇

• X₁₈₆₁ = complement of X₃₁₀₀

• X₁₈₆₁ = crossdifference of every pair of points on line X₄₈X₁₄₅₉

• X₁₈₆₁ = inverse-in-circumconic-centered-at-X₉ of X₁₉

• X₁₈₆₁ = pole wrt polar circle of trilinear polar of X₆₇₃ (line X₁X₅₁₄)

• X₁₈₆₁ = X₄₈-isoconjugate (polar conjugate) of X₆₇₃

• X₁₈₆₁ = perspector of circumconic through the polar conjugates of PU(47) and PU(51)

• X₁₈₆₁ = X₈₀₇₆-of-orthic-triangle if ABC is acute

• X₁₈₆₁ = X₆₃-isoconjugate of X₁₄₃₈