X909

POINT ADHAFERA

X909 = trilinear pole of line X31X663
< 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) { 9, 48 }: Central Line L(9, 48) { 55, 184 }: Central Line L(55, 184) { 163, 284 }: Central Line L(163, 284) { 19, 604 }: Central Line L(19, 604) { 333, 662 }: Central Line L(333, 662) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_9 = MITTENPUNKT (0.5110, 0.1615) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_19 = CLAWSON POINT (0.6246, 0.4244) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_909 = POINT ADHAFERA (0.9286, -0.3499) A B C X908 X9 X48 X55 X184 X163 X284 X19 X604 X333 X662 X909 (a, b, c) = (5, 6, 7) | AB = 1

X909 (POINT ADHAFERA) 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 \(f(a,b,c) = a/[(wb + vc)/a - v - w]\),\(u : v : w\) = X3
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-9.634392551591\)
▸ Incident Central Lines5 lines

{9, 48}, {19, 604}, {55, 184}, {163, 284}, {333, 662}

▸ Functional Relations6 relations