X₂₉₃₇

TANGENTIAL-ISOGONAL CONJUGATE OF X₁₉₅

X₂₉₃₇ is the tangential-isogonal conjugate of X₁₉₅.

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

X₂₉₃₇ (TANGENTIAL-ISOGONAL CONJUGATE OF X₁₉₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {184, 195}

• Related Centers: X₂₅₀ (ISOGONAL CONJUGATE OF X₁₂₅), X₉₃₀ (ANTICOMPLEMENT OF X₁₃₇), X₂ (CENTROID), X₃ (CIRCUMCENTER), X₁₈₄ (INVERSE OF X), X₁₉₅ (-CEVA CONJUGATE OF X₃)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as described just before X₂₈₈₃

Barycentrics: \(a^{2} (a^{8} - 2 a^{6} (b^{2} + c^{2}) - a^{4} b^{2} c^{2} + a^{2} (2 b^{6} + b^{4} c^{2} + b^{2} c^{4} + 2 c^{6}) - (b^{2} - c^{2})^{2} (b^{4} + c^{4})) : :\)

Search Value (6, 9, 13): \(-7.060626179682\)

▸ Incident Central Lines9 lines

{2, 3}, {15, 2927}, {16, 2928}, {49, 511}, {182, 2916}, {184, 195}, {399, 2917}, {1154, 1614}, {1216, 1495}

▸ Functional Relations5 relations

• X₂₉₃₇ = crosspoint of X₂₅₀ and X₉₃₀

• X₂₉₃₇ = crosssum of X₁₂₅ and X₁₅₁₀

• X₂₉₃₇ = circumcircle-inverse of X₃₇₉₃₈

• X₂₉₃₇ = X₃₅-of-tangential-triangle if ABC is acute

• X₂₉₃₇ = {X₃,X₂₆}-harmonic conjugate of X₂₀₇₀

Notes

As a point on the Euler line, X₂₉₃₇ has Shinagawa coefficients \((27E^{3} + 144E^{2}F + 240EF^{2} + 128F^{3} - 48(3E + 8F)S^{2}, -63E^{3} - 240E^{2}F - 304EF^{2} - 128F^{3} + 48(7E + 8F)S^{2})\).