X2652

TRILINEAR POLE OF PU(81)

X2652 = isogonal conjugate of X2651
< 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) { 243, 415 }: Central Line L(243, 415) { 409, 662 }: Central Line L(409, 662) { 3, 1247 }: Central Line L(3, 1247) { 897, 1155 }: Central Line L(897, 1155) { 759, 1326 }: Central Line L(759, 1326) { 19, 2305 }: Central Line L(19, 2305) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2651 = CROSSDIFFERENCE OF PU(81) (6.8757, 8.5193) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_415 = -HIRST INVERSE OF X(29) (0.7758, 0.8236) X_409 = EULER X(21)-1st-SUBSTITUTION POINT (0.5419, 0.2117) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1247 = ISOGONAL CONJUGATE OF X(1046) (0.4342, 0.1331) X_897 = ISOGONAL CONJUGATE OF X(896) (0.9765, -0.0384) X_1155 = SCHRÖDER POINT (1.7143, 2.3328) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_1326 = INVERSE-IN-CIRCUMCIRCLE OF X(58) (1.1309, 1.1440) X_19 = CLAWSON POINT (0.6246, 0.4244) X_2305 = -ISOCONJUGATE OF X(1247) (0.6601, 0.3665) X_2652 = TRILINEAR POLE OF PU(81) (0.9537, -0.1117) A B C X2651 X243 X415 X409 X662 X3 X1247 X897 X1155 X759 X1326 X19 X2305 X2652 (a, b, c) = (5, 6, 7) | AB = 1

X2652 (TRILINEAR POLE OF PU(81)) 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 \(f(a,b,c) = (\cos B + \cos C)/(\cos^{2} B + \cos^{2} C - \cos^{2} A + \cos B \cos C - \cos C \cos A - \cos A \cos B)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.758202836300\)
▸ Incident Central Lines8 lines

{1, 2648}, {3, 1247}, {19, 2305}, {243, 415}, {409, 662}, {759, 1326}, {897, 1155}, {1910, 2182}

▸ Functional Relations1 relation