X2640

CROSSSUM OF PU(78)

X2640 = crosspoint of PU(79)
< 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) { 1, 662 }: Central Line L(1, 662) { 45, 846 }: Central Line L(45, 846) { 3, 1247 }: Central Line L(3, 1247) { 19, 1581 }: Central Line L(19, 1581) { 610, 1910 }: Central Line L(610, 1910) { 1045, 1781 }: Central Line L(1045, 1781) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1247 = ISOGONAL CONJUGATE OF X(1046) (0.4342, 0.1331) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_1910 = TRILINEAR POLE OF PU(23) (0.9516, -0.2978) X_1045 = -CEVA CONJUGATE OF X(1) (0.6065, 0.2647) X_1781 = MIMOSA TRANSFORM OF X(1214) (0.5847, 0.2809) X_2640 = CROSSSUM OF PU(78) (1.3971, -0.3206) A B C X1 X662 X45 X846 X3 X1247 X19 X1581 X610 X1910 X1045 X1781 X2640 (a, b, c) = (5, 6, 7) | AB = 1

X2640 (CROSSSUM OF PU(78)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cot A - \cot B)(\cot A - \cot C) - (\cot B - \cot C)^{2} : :\)
Search Value (6, 9, 13): \(1.046288391159\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{4} - b^{4} - c^{4} + 3b^{2}c^{2} -a^{2}b^{2} - a^{2}c^{2} : :\) (M. Iliev, 5/13/07)

▸ Incident Central Lines9 lines

{1, 662}, {3, 1247}, {9, 2645}, {19, 1581}, {45, 846}, {610, 1910}, {1045, 1781}, {1580, 2173}, {1707, 2247}

▸ Functional Relations1 relation

  • X2640 = crosspoint of PU(79)