X1926

CROSSDIFFERENCE OF PU(13)

X1926 = X1934-Ceva conjugate of X1925
< 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) { 38, 75 }: Central Line L(38, 75) { 76, 257 }: Central Line L(76, 257) { 661, 786 }: Central Line L(661, 786) { 799, 1755 }: Central Line L(799, 1755) { 1590, 1636 }: Central Line L(1590, 1636) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1927 = TRILINEAR POLE OF PU(13) (0.9865, 0.0569) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_786 = ODD (- 3, - 1) INFINITY POINT (0.0039, 0.4444) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_1755 = MIMOSA TRANSFORM OF X(287) (1.5943, 2.3982) X_1590 = POINT CHARA II (0.4905, 0.0773) X_1636 = TRIPOLAR CENTROID OF X(3) (-3.1554, -0.2797) X_1926 = CROSSDIFFERENCE OF PU(13) (-0.6825, -0.5956) A B C X1927 X38 X75 X76 X257 X661 X786 X799 X1755 X1590 X1636 X1926 (a, b, c) = (5, 6, 7) | AB = 1

X1926 (CROSSDIFFERENCE OF PU(13)) 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 \(f(a,b,c) = 1 - b^{2}c^{2}/a^{4}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.046631846137\)
▸ Incident Central Lines5 lines

{38, 75}, {76, 257}, {661, 786}, {799, 1755}, {1590, 1636}

▸ Functional Relations7 relations