X₂₉₅₁

EXCENTRAL-ISOGONAL CONJUGATE OF X₅₇

X₂₉₅₁ is the excentral-isogonal conjugate of X₅₇.

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

X₂₉₅₁ (EXCENTRAL-ISOGONAL CONJUGATE OF X₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 7}, {9, 165}

• Related Centers: X₅₇ (ISOGONAL CONJUGATE OF X₉), X₁ (INCENTER), X₇ (GERGONNE POINT), X₉ (MITTENPUNKT), X₁₆₅ (CENTROID OF THE EXCENTRAL TRIANGLE)

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

Search Value (6, 9, 13): \(18.295197668868\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = \tan^{2}(B/2) + \tan^{2}(C/2) - \tan^{2}(A/2)\) (Randy Hutson, 9/23/2011)

▸ Linear Combinations1 combination

• X₂₉₅₁ = \(R_{a}\) J_a + \(R_{b}\) J_b + \(R_{c}\) J_c, where J_a, J_b, J_c are excenters, and \(R_{a}\), \(R_{b}\), \(R_{c}\) are the exradii

▸ Incident Central Lines13 lines

{1, 7}, {9, 165}, {40, 971}, {63, 2942}, {142, 1699}, {144, 200}, {166, 167}, {191, 2938}, {518, 2136}, {610, 1633}, {1050, 1740}, {1158, 2949}, {1292, 2371}

▸ Functional Relations9 relations

• X₂₉₅₁ = X_i-Ceva conjugate of X_j for these (i,j): (144, 9), (200, 1)

• X₂₉₅₁ = isogonal conjugate of X₈₉₁₇

• X₂₉₅₁ = X₆₉-of-excentral-triangle

• X₂₉₅₁ = excentral isotomic conjugate of X₁

• X₂₉₅₁ = perspector of the excentral inconic with center X₄₀

• X₂₉₅₁ = antipedal isotomic conjugate of X₁

• X₂₉₅₁ = X₇-of-3rd-antipedal-triangle-of-X₁

• X₂₉₅₁ = ABC-to-excentral barycentric image of X₇

• X₂₉₅₁ = X_i-aleph conjugate of X_j for these (i,j): (2, 1445), (9, 1), (55, 1740), (100, 651), (188, 57), (200, 2951), (259, 978), (281, 920), (312, 1760), (318, 1748), (643, 662), (644, 100), (650, 1052), (664, 658), (1897, 653), (2287, 411), (2322, 412)