X3730

X1212com(EXCENTRAL TRIANGLE)

X3730 = trilinear pole wrt 1st circumperp triangle of antiorthic axis
< 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, 9 }: Orthocenter–Spieker Line { 35, 41 }: Central Line L(35, 41) { 3, 101 }: Central Line L(3, 101) { 76, 190 }: Central Line L(76, 190) { 55, 218 }: Central Line L(55, 218) { 165, 170 }: Central Line L(165, 170) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_170 = -ALEPH CONJUGATE OF X(9) (0.4465, -0.0557) X_3730 = com(EXCENTRAL TRIANGLE) (0.4910, 0.1153) A B C X4 X9 X35 X41 X3 X101 X76 X190 X55 X218 X165 X170 X3730 (a, b, c) = (5, 6, 7) | AB = 1

X3730 (X1212com(EXCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2}(b^{2} + c^{2} - ab - ac + bc) : :\)
Search Value (6, 9, 13): \(4.952016915506\)
▸ Incident Central Lines33 lines

{1, 672}, {2, 2140}, {3, 101}, {4, 9}, {6, 595}, {8, 1018}, {35, 41}, {37, 579}, {39, 995}, {45, 2245}, {55, 218}, {76, 190}, {165, 170}, {213, 386}, {219, 572}, {284, 2911}, {348, 1025}, {514, 3177}, {517, 1212}, {519, 3208}, {644, 2975}, {813, 1083}, {910, 3579}, {993, 2329}, {1011, 3190}, {1030, 3204}, {1400, 3339}, {1726, 3219}, {1743, 2269}, {2203, 2328}, {2260, 3247}, {2267, 2323}, {2275, 3230}

▸ Functional Relations5 relations