X₂₂₉₉

X₂-ISOCONJUGATE OF X₁₂₁₄

X₂₂₉₉ = crosssum of X₇₂ and X₁₂₁₄

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

X₂₂₉₉ (X₂-ISOCONJUGATE OF X₁₂₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 25}, {9, 33}

• Related Centers: X₆ (SYMMEDIAN POINT), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₉ (MITTENPUNKT), X₃₃ (PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₂₁₄

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(29.409712594232\)

▸ Incident Central Lines25 lines

{4, 580}, {6, 25}, {9, 33}, {19, 31}, {21, 1039}, {24, 581}, {27, 162}, {28, 34}, {29, 270}, {42, 2259}, {55, 607}, {73, 2360}, {112, 2291}, {238, 1848}, {284, 2189}, {909, 2206}, {1104, 1829}, {1174, 2356}, {1333, 1436}, {1402, 1945}, {1435, 1471}, {1824, 2161}, {1841, 2160}, {1859, 2361}, {1973, 2258}

▸ Functional Relations8 relations

• X₂₂₉₉ = X_i-Ceva conjugate of X_j for these (i,j): (28, 1474), (29, 284), (270, 1172), (1172, 2332), (2189, 2204)

• X₂₂₉₉ = cevapoint of X_i and X_j for these (i,j): (23, 31), (607, 2212)

• X₂₂₉₉ = X_i-cross conjugate of X_j for these (i,j): (31, 2194), (607, 1172), (2204, 1474), (2212, 2204)

• X₂₂₉₉ = crosspoint of X_i and X_j for these (i,j): (28, 1172), (270, 2189)

• X₂₂₉₉ = crosssum of X₇₂ and X₁₂₁₄

• X₂₂₉₉ = isogonal conjugate of X₃₀₇

• X₂₂₉₉ = polar conjugate of X₃₄₉

• X₂₂₉₉ = crossdifference of every pair of points on line X₅₂₅X₈₆₁₁