X1951

CROSSDIFFERENCE OF PU(20)

X1951 = X1949-Ceva conjugate of X1950
< 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) { 6, 41 }: Central Line L(6, 41) { 21, 270 }: Central Line L(21, 270) { 104, 294 }: Central Line L(104, 294) { 19, 577 }: Central Line L(19, 577) { 3, 607 }: Central Line L(3, 607) { 652, 663 }: Central Line L(652, 663) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_19 = CLAWSON POINT (0.6246, 0.4244) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_652 = CROSSDIFFERENCE OF X(1) AND X(4) (7.2558, -0.6836) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_1951 = CROSSDIFFERENCE OF PU(20) (3.2396, 6.6676) A B C X2 X6 X41 X21 X270 X104 X294 X19 X577 X3 X607 X652 X663 X1951 (a, b, c) = (5, 6, 7) | AB = 1

X1951 (CROSSDIFFERENCE OF PU(20)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(\cos^{2} A - \cos B \cos C) : :\)
Search Value (6, 9, 13): \(7.356619709325\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a (a - b - c) (a^{4} - a^{2} (b^{2} - b c + c^{2}) - b c (b - c)^{2}) : :\)

▸ Incident Central Lines12 lines

{1, 1729}, {3, 607}, {6, 41}, {19, 577}, {21, 270}, {104, 294}, {517, 906}, {652, 663}, {851, 1430}, {910, 1415}, {1262, 1465}, {1409, 1630}

▸ Functional Relations8 relations