X2378

CIR(X530)

X2378 = 2nd-Parry-to-ABC similarity image of X15
< 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) { 15, 110 }: Central Line L(15, 110) { 99, 298 }: Central Line L(99, 298) { 14, 476 }: Central Line L(14, 476) { 16, 691 }: Central Line L(16, 691) { 512, 2379 }: Central Line L(512, 2379) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_530 = DIRECTION OF VECTOR AX + BX + CX, where X = X(13) (0.8451, 0.6997) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_99 = STEINER POINT (0.1109, 0.4322) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_476 = TIXIER POINT (0.9824, 0.2685) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_2379 = CIR(X(531)) (0.0300, 0.3009) X_2378 = CIR(X(530)) (0.8940, -0.2222) A B C X530 X15 X110 X99 X298 X14 X476 X16 X691 X512 X2379 X2378 (a, b, c) = (5, 6, 7) | AB = 1

X2378 (CIR(X530)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(F(u,v,w) : F(v,w,u) : F(w,u,v)\), where F is as indicated just before X2365, and \(u : v : w\) = X530
Search Value (6, 9, 13): \(8.580687751616\)

X2378 lies on the circumcircle.

▸ Incident Central Lines5 lines

{14, 476}, {15, 110}, {16, 691}, {99, 298}, {512, 2379}

▸ Functional Relations3 relations