X1098

TRILINEAR SQUARE OF X21

X1098 = isogonal conjugate of X1254
< 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) { 21, 60 }: Central Line L(21, 60) { 58, 86 }: Central Line L(58, 86) { 29, 270 }: Central Line L(29, 270) { 65, 409 }: Central Line L(65, 409) { 8, 643 }: Central Line L(8, 643) { 3, 662 }: Central Line L(3, 662) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1254 = ISOGONAL CONJUGATE OF X(1098) (0.6258, 0.3523) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_409 = EULER X(21)-1st-SUBSTITUTION POINT (0.5419, 0.2117) X_8 = NAGEL POINT (0.4694, 0.1333) X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA (0.0142, 0.3704) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_1098 = TRILINEAR SQUARE OF X(21) (0.4785, 0.1286) A B C X1254 X21 X60 X58 X86 X29 X270 X65 X409 X8 X643 X3 X662 X1098 (a, b, c) = (5, 6, 7) | AB = 1

X1098 (TRILINEAR SQUARE OF X21) 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 \(f(A,B,C) = 1/(\cos B + \cos C)^{2}\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(4.244563329859\)
▸ Incident Central Lines7 lines

{3, 662}, {8, 643}, {21, 60}, {29, 270}, {58, 86}, {65, 409}, {81, 1104}

▸ Functional Relations2 relations