X1958

CROSSSUM OF PU(23)

X1958 = cevapoint of X610 and X1740
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 48, 75 }: Central Line L(48, 75) { 19, 326 }: Central Line L(19, 326) { 63, 610 }: Central Line L(63, 610) { 239, 604 }: Central Line L(239, 604) { 41, 894 }: Central Line L(41, 894) { 100, 1253 }: Central Line L(100, 1253) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_1740 = MIMOSA TRANSFORM OF X(184) (0.7017, 0.3500) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_19 = CLAWSON POINT (0.6246, 0.4244) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1253 = ISOGONAL CONJUGATE OF X(1088) (0.5237, 0.1548) X_1958 = CROSSSUM OF PU(23) (0.4653, 0.2026) A B C X610 X1740 X48 X75 X19 X326 X63 X239 X604 X41 X894 X100 X1253 X1958 (a, b, c) = (5, 6, 7) | AB = 1

X1958 (CROSSSUM OF PU(23)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cot^{2} A + \cot B \cot C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.845619550216\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{4} - a^{2}b^{2} - a^{2}c^{2} + 2b^{2}c^{2}\) (M. Iliev, 5/13/2007)

  • Trilinears: \(S_{A}\)\(S_{A}\) + \(S_{B}\)\(S_{C}\) : \(S_{B}\)\(S_{B}\) + \(S_{C}\)\(S_{A}\) : \(S_{C}\)\(S_{C}\) + \(S_{A}\)\(S_{B}\) (C. Lozada, 9/07/2013)

  • Trilinears: \(a^{2}S_{A} - b^{2}c^{2} : b^{2}S_{B} - c^{2}a^{2} : c^{2}S_{C} - a^{2}b^{2}\) (C. Lozada, 9/07/2013)

▸ Incident Central Lines7 lines

{19, 326}, {31, 1582}, {41, 894}, {48, 75}, {63, 610}, {100, 1253}, {239, 604}

▸ Functional Relations2 relations