X1921

CROSSDIFFERENCE OF PU(12)

X1921 = X334-Ceva conjugate of X1920
< 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) { 10, 75 }: Central Line L(10, 75) { 37, 308 }: Central Line L(37, 308) { 2, 561 }: Central Line L(2, 561) { 350, 740 }: Central Line L(350, 740) { 518, 668 }: Central Line L(518, 668) { 274, 1107 }: Central Line L(274, 1107) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1922 = TRILINEAR POLE OF PU(12) (0.9912, 0.0547) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) X_2 = CENTROID (0.5374, 0.2000) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_1107 = CROSSPOINT OF X(1) AND X(274) (0.5495, 0.2072) X_1921 = CROSSDIFFERENCE OF PU(12) (-1.0027, -0.8795) A B C X1922 X10 X75 X37 X308 X2 X561 X350 X740 X518 X668 X274 X1107 X1921 (a, b, c) = (5, 6, 7) | AB = 1

X1921 (CROSSDIFFERENCE OF PU(12)) 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 \(f(a,b,c) = b^{3}c^{3}(a^{2} - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(11.581311522770\)
▸ Incident Central Lines6 lines

{2, 561}, {10, 75}, {37, 308}, {274, 1107}, {350, 740}, {518, 668}

▸ Functional Relations6 relations