X1968

CROSSSUM OF PU(37)

X1968 = X1976-Ceva conjugate of X232
< 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) { 4, 32 }: Central Line L(4, 32) { 6, 64 }: Central Line L(6, 64) { 33, 172 }: Central Line L(33, 172) { 24, 187 }: Central Line L(24, 187) { 3, 232 }: Central Line L(3, 232) { 20, 393 }: Central Line L(20, 393) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1976 = TRILINEAR POLE OF PU(39) (1.0272, -0.3962) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_4 = ORTHOCENTER (0.6122, 0.3958) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_1968 = CROSSSUM OF PU(37) (0.5947, 0.4354) A B C X1976 X232 X4 X32 X6 X64 X33 X172 X24 X187 X3 X20 X393 X1968 (a, b, c) = (5, 6, 7) | AB = 1

X1968 (CROSSSUM OF PU(37)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(\tan^{2} A + \tan B \tan C) : :\)
Search Value (6, 9, 13): \(-0.609717631532\)
▸ Alternate Coordinates1 form

  • Trilinears: \(2 \cos A + \sin A (\tan A - \cot \omega ) : :\)

▸ Incident Central Lines16 lines

{3, 232}, {4, 32}, {6, 64}, {20, 393}, {24, 187}, {25, 1611}, {33, 172}, {39, 378}, {53, 571}, {194, 648}, {217, 578}, {230, 235}, {264, 384}, {1147, 1625}, {1384, 1598}, {1691, 1974}

▸ Functional Relations4 relations