X₁₉₉₃

ORTHOCORRESPONDENT OF X₃

X₁₉₉₃ = reflection of X₂₂ in X₁₈₄

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

X₁₉₉₃ (ORTHOCORRESPONDENT OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {22, 184}

• Related Centers: X₂₂ (EXETER POINT), X₁₈₄ (INVERSE OF X)

Trilinears: \(\csc A \cos 2A : \csc B \cos 2B : \csc C \cos 2C\)

Barycentrics: \(\cos 2A : \cos 2B : \cos 2C\)

Search Value (6, 9, 13): \(13.265713221005\)

▸ Alternate Coordinates3 forms

• Barycentrics: \(a^{2} - 2 R^{2} : :\)

• Barycentrics: \(2 \cos^{2} A - 1 : :\)

• Barycentrics: \(2 \sin^{2} A - 1 : :\)

▸ Incident Central Lines32 lines

{2, 6}, {3, 54}, {4, 155}, {20, 1181}, {22, 184}, {23, 154}, {24, 52}, {25, 110}, {26, 49}, {51, 576}, {63, 2003}, {68, 1594}, {194, 401}, {219, 3219}, {222, 3218}, {264, 275}, {278, 651}, {283, 581}, {317, 467}, {371, 1599}, {372, 1600}, {389, 1092}, {399, 1539}, {458, 1235}, {493, 588}, {494, 589}, {569, 1216}, {573, 1790}, {631, 1199}, {858, 1899}, {1196, 1570}, {1353, 1368}

▸ Functional Relations13 relations

• X₁₉₉₃ = reflection of X₂₂ in X₁₈₄

• X₁₉₉₃ = isogonal conjugate of X₂₁₆₅

• X₁₉₉₃ = isotomic conjugate of X₅₃₉₂

• X₁₉₉₃ = polar conjugate of X₈₄₇

• X₁₉₉₃ = {X₂,X₆}-harmonic conjugate of X₅₄₂₂

• X₁₉₉₃ = crosspoint of X₆ and X₁₅₅ wrt both the excentral and tangential triangles

• X₁₉₉₃ = X₆-isoconjugate of X₉₁

• X₁₉₉₃ = X₉₂-isoconjugate of X₂₃₅₁

• X₁₉₉₃ = anticomplement of X₃₄₃

• X₁₉₉₃ = X_i-Ceva conjugate of X_j for these (i,j): (264, 3), (275, 2), (317, 24), (1585, 1599), (1586, 1600)

• X₁₉₉₃ = cevapoint of X_i and X_j for these (i,j): (6, 155), (571, 1147)

• X₁₉₉₃ = crosspoint of X_i and X_j for these (i,j): (249, 648), (1585, 1586)

• X₁₉₉₃ = crosssum of X₁₁₅ and X₆₄₇