X1943

CROSSSUM OF PU(18)

< 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) { 57, 239 }: Central Line L(57, 239) { 75, 222 }: Central Line L(75, 222) { 69, 278 }: Central Line L(69, 278) { 92, 394 }: Central Line L(92, 394) { 2, 914 }: Central Line L(2, 914) { 321, 651 }: Central Line L(321, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_2 = CENTROID (0.5374, 0.2000) X_914 = ISOGONAL CONJUGATE OF X(913) (-2.5447, -1.0613) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_1943 = CROSSSUM OF PU(18) (0.4713, 0.1729) A B C X57 X239 X75 X222 X69 X278 X92 X394 X2 X914 X321 X651 X1943 (a, b, c) = (5, 6, 7) | AB = 1

X1943 (CROSSSUM OF PU(18)) 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 \(f(a,b,c) = bc(\cos^{2} A + \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.231082000367\)
▸ Incident Central Lines11 lines

{2, 914}, {57, 239}, {69, 278}, {75, 222}, {81, 1441}, {92, 394}, {225, 1330}, {321, 651}, {333, 664}, {637, 1659}, {1231, 1396}