X172

TRILINEAR PRODUCT X6*X171

X172 = X101-beth conjugate of X172
< 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) { 1, 32 }: Central Line L(1, 32) { 6, 41 }: Central Line L(6, 41) { 21, 37 }: Central Line L(21, 37) { 36, 39 }: Central Line L(36, 39) { 58, 101 }: Central Line L(58, 101) { 35, 187 }: Central Line L(35, 187) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) A B C X257 X1 X32 X6 X41 X21 X37 X36 X39 X58 X101 X35 X187 X172 (a, b, c) = (5, 6, 7) | AB = 1

X172 (TRILINEAR PRODUCT X6*X171) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{3} + abc : b^{3} + abc : c^{3} + abc\)
Barycentrics: \(a^{4} + bca^{2} : b^{4} + cab^{2} : c^{4} + abc^{2}\)
Search Value (6, 9, 13): \(0.774827726345\)
▸ Incident Central Lines13 lines

{1, 32}, {6, 41}, {12, 230}, {21, 37}, {35, 187}, {36, 39}, {42, 199}, {58, 101}, {65, 248}, {350, 384}, {577, 1038}, {694, 904}, {699, 932}

▸ Functional Relations8 relations